Accelerating Branes and Brane Temperature (2008)
We define the local acceleration and jerk of a relativistic brane in an ambient spacetime, and construct from them a dimensionless parameter lambda that must be small for an interpretation of brane...
Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence (2006)
Skenderis, K., Townsend, P. K.
The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain wall solution that admits a Killing spinor is shown to correspond to a...
Self-gravitating Yang Monopoles in all Dimensions (2006)
Gibbons, G. W., Townsend, P. K.
The (2k+2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k) (or SU(2) for k=2 and SU(3) for k=3) are shown to admit a family of spherically-symmetric magnetic monopole solutions, for...
Supersymmetric regularization and superconformal anomalies (2005)
The authors review the status of dimensional regularization by dimensional reduction as a regularization scheme for supersymmetric field theories with particular emphasis on the calculation of the...
Classical resolution of singularities in dilaton cosmologies (2005)
Bergshoeff, E. A., Collinucci, A., Roest, D., Russo, J. G., Townsend, P. K.
For models of dilaton-gravity with a possible exponential potential, such as the tensor-scalar sector of IIA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne...
Cosmological D-instantons and Cyclic Universes (2005)
Bergshoeff, E. A., Collinucci, A., Roest, D., Russo, J. G., Townsend, P. K.
For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the `augmented target space' connect FLRW...
Cosmological D-instantons and cyclic universes (2005)
Roest, D., Collinucci, A., Bergshoeff, E.A., Russo, J.G., Townsend, P.K.
For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the ‘augmented target space’ connect FLRW...
Classical resolution of singularities in dilaton cosmologies (2005)
Roest, D., Collinucci, A., Bergshoeff, E.A., Russo, J.G., Townsend, P.K.
For models of dilaton gravity with a possible exponential potential, such as the tensor–scalar sector of IIA supergravity, we show how cosmological solutions correspond to trajectories in a 2D...
String and M-theory Deformations of Manifolds with Special Holonomy (2004)
Lu, H., Pope, C. N., Stelle, K. S., Townsend, P. K.
The R^4-type corrections to ten and eleven dimensional supergravity required by string and M-theory imply corrections to supersymmetric supergravity compactifications on manifolds of special...
Cosmology as Relativistic Particle Mechanics: From Big Crunch to Big Bang (2004)
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application,...
Lu, H., Pope, C. N., Stelle, K. S., Townsend, P. K.
The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of $G_2$ holonomy, but these supergravity vacua are deformed away from special holonomy by the...
Sigma-model soliton intersections from exceptional calibrations (2002)
Portugues, R., Townsend, P. K.
A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular...
Quintessence from M-Theory (2001)
The status of exponential scalar potentials in supergravity is reviewed, and updated. One version of N=8 D=4 supergravity with a positive exponential potential, obtainable from a...
It is shown that a IIA superstring carrying D0-brane charge can be `blown-up', in a {\it Minkowski vacuum} background, to a (1/4)-supersymmetric tubular D2-brane, supported against collapse by the...
The Heterotic Dyonic Instanton (2000)
Eyras, E., Townsend, P. K., Zamaklar, M.
The static Yang-Mills-Higgs dyonic instanton is shown to have a non-vanishing, but anti-self-dual, angular momentum 2-form with skew eigenvalues equal to the electric charge; for large charge the...
M-brane interpolations and (2,0) Renormalization Group flow (2000)
Bergshoeff, E., Cai, R-G., Ohta, N., Townsend, P. K.
We obtain the M5-M2-MW bound state solutions of 11-dimensional supergravity corresponding to the 1/2 supersymmetric vacua of the M5-brane equations with constant background fields. In the...
Field theories that describe {\sl small} fluctuations of branes are limits of `brane theories' that describe {\sl large} fluctuations. In particular, supersymmetric sigma-models arise in this way....
PhreMology--calibrating M-branes (1999)
The relevance of calibrations, and `generalized' calibrations, to supersymmetric M-brane configurations, and their associated field theories, is reviewed, with emphasis on applications to domain...
A Bogomol`nyi equation for intersecting domain walls (1999)
We argue that the Wess-Zumino model with quartic superpotential admits static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show that...
Supersymmetry and generalized calibrations (1999)
Gutowski, J., Papadopoulos, G., Townsend, P. K.
A static minimal energy configuration of a super p-brane in a supersymmetric (n+1)-dimensional spacetime is shown to be a `generalized calibrated' submanifold. Calibrations in $\bE^{(1,n)}$ and...
Solitons on the Supermembrane (1999)
Bergshoeff, E., Townsend, P. K.
Energy bounds are derived for planar and compactified M2-branes in a hyper-K\"ahler background. These bounds are saturated, respectively, by lump and Q-kink solitons, which are shown to preserve a...
The M(atrix) model/adS_2 correspondence (1999)
The M(atrix) model has a dual realization as IIA superstring theory in the near-horizon geometry of the supergravity D0-brane. The role of $adS_2$ in this correspondence is reviewed, and some aspects...
Killing spinors, supersymmetries and rotating intersecting branes (1999)
I review a recently proposed method for determining the symmetry superalgebra of a supergravity configuration from its Killing spinors, and its application to the `near-horizon' limits of various...
Black Holes and Calogero Models (1998)
Gibbons, G. W., Townsend, P. K.
We argue that the large $n$ limit of the $n$-particle $SU(1,1|2)$ superconformal Calogero model provides a microscopic description of the extreme Reissner-Nordstr{\"o}m black hole in the near-horizon...
Superconformal mechanics, black holes, and non-linear realizations (1998)
De Azcarraga, J. A., Izquierdo, J. M., Bueno, J. C. Perez, Townsend, P. K.
The OSp(2|2)-invariant planar dynamics of a D=4 superparticle near the horizon of a large mass extreme black hole is described by an N=2 superconformal mechanics, with the SO(2) charge being the...
Black Holes of D=5 Supergravity (1998)
Gauntlett, J. P., Myers, R. C., Townsend, P. K.
We discuss some general features of black holes of five-dimensional supergravity, such as the first law of black hole mechanics. We also discuss some special features of rotating supersymmetric black...
The domain-wall/QFT correspondence (1998)
Boonstra, H. J., Skenderis, K., Townsend, P. K.
We extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge...
The M5-brane Hamiltonian (1998)
Bergshoeff, E., Sorokin, D., Townsend, P. K.
We obtain the Hamiltonian form of the worldvolume action for the M5-brane in a general D=11 supergravity background. We use this result to obtain a new version of the covariant M5-brane Lagrangian in...
Black Holes and Superconformal Mechanics (1998)
Claus, P., Derix, M., Kallosh, R., Kumar, J., Townsend, P. K., Van Proeyen, A.
The dynamics of a (super)particle near the horizon of an extreme Reissner-Nordstrom black hole is shown to be governed by an action that reduces to a (super)conformal mechanics model in the limit of...
Super D-branes revisited (1998)
Bergshoeff, E., Townsend, P. K.
A version of the kappa-symmetric super D-p-brane action is presented in which the tension is a dynamical variable, equal to the flux of a p-form worldvolume gauge field. The Lagrangian is shown to be...
Conformal Theory of M2, D3, M5 and `D1+D5' Branes (1998)
Claus, P., Kallosh, R., Kumar, J., Townsend, P. K., Van Proeyen, A.
The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from...
Gauged Supergravity Vacua From Intersecting Branes (1998)
Cowdall, P. M., Townsend, P. K.
Domain wall and electrovac solutions of gauged N=4 D=4 supergravity, with gauge group SU(2) or SU(2)xSU(2), are interpreted as supersymmetric Kaluza-Klein vacua of N=1 D=10 supergravity. These vacua...
Super D-branes revisited (1998)
Townsend, P.K., Bergshoeff, E.
A version of the κ-symmetric super Dp-brane action is presented in which the tension is a dynamical variable, equal to the flux of a p-form world-volume gauge field. The Lagrangian is shown to be...
The M5-brane Hamiltonian (1998)
Townsend, P.K., Sorokin, D., Bergshoeff, E.
We obtain the Hamiltonian form of the world-volume action for the M5-brane in a general D = 11 supergravity background. We use this result to obtain a new version of the covariant M5-brane Lagrangian...
M-theory from its superalgebra (1997)
These lectures explore what can be learnt about M-theory from its superalgebra. The first three lectures introduce the 'basic' branes of M-theory, and type II superstring theories, and show how the...
The Manifestly Sl(2;Z)-covariant Superstring (1997)
Cederwall, M., Townsend, P. K.
We present a manifestly Sl(2;Z)-covariant action for the type IIB superstring, and prove kappa-symmetry for on-shell IIB supergravity backgrounds.
Supersymmetric configurations of non-orthogonally intersecting M-5-branes can be obtained by rotation of one of a pair of parallel M-5-branes. Examples preserving 1/4, 3/16 and 1/8 supersymmetry are...
M(embrane) theory on $T^9$ (1997)
An `algebraic' approach to M-theory is briefly reviewed, and a proposal is made for a similar algebraic structure underlying the $T^9$ compactification of `M(embrane) theory', i.e. the M(atrix) model...
Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP, Cambridge. The course covers some of the developments in Black Hole physics of the 1960s and 1970s.
Massive IIA supergravity from the topologically massive D-2-brane (1997)
Bergshoeff, E., Cowdall, P. M., Townsend, P. K.
The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by $\kappa$-symmetry of the topologically massive D-2-brane.
Membrane tension and manifest IIB S-duality (1997)
A manifestly S-dual, and `12 dimensional', IIB superstring action with an $Sl(2;\bR)$ doublet of `Born-Infeld' fields is presented. The M-theory origin of the 12th dimension is the M-2-brane tension,...
Hyper-Kahler manifolds and multiply-intersecting branes (1997)
Gauntlett, J. P., Gibbons, G. W., Papadopoulos, G., Townsend, P. K.
Generalized membrane solutions of D=11 supergravity, for which the transverse space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals representing the intersection of parallel...
Townsend, P.K., Bergshoeff, E.
We present a manifestly Lorentz invariant, space-time supersymmetric, and 'κ-invariant' world-volume action for all type II Dirichlet p-branes, p ≤ 9, in a general type II supergravity background,...
Massive IIA supergravity from the topologically massive D-2-brane (1997)
Townsend, P.K., Cowdall, P.M., Bergshoeff, E.
The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by κ-symmetry of the topologically massive D-2-brane.
Four Lectures on M-theory (1996)
Synopsis: (i) how superstring theories are unified by M-theory; (ii) how superstring and supermembrane properties follow from the D=10 and D=11 supersymmetry algebras; (iii) how D=10 and D=11...
Bergshoeff, E., Townsend, P. K.
We present a manifestly Lorentz invariant, spacetime supersymmetric, and `$\kappa$-invariant' worldvolume action for all type II Dirichlet p-branes, $p\le9$, in a general type II supergravity...
Some aspects of the role of p-branes in non-perturbative superstring theory and M-theory are reviewed. It is then shown how the Chern-Simons terms in D=10 and D=11 supergravity theories determine...
Kaluza-Klein on the Brane (1996)
Papadopoulos, G., Townsend, P. K.
The M-theory interpretation of certain D=10 IIA p-branes implies the existence of worldvolume Kaluza-Klein modes which are expected to appear as 0-brane/p-brane bound states preserving 1/4 of the...
Domain Walls in Massive Supergravities (1996)
Cowdall, P. M., Lu, H., Pope, C. N., Stelle, K. S., Townsend, P. K.
We show how toroidally-compactified eleven-dimensional supergravity can be consistently truncated to yield a variety of maximally-supersymmetric ``massive'' supergravities in spacetime dimensions...
Domain Walls from Anti-de Sitter Spacetime (1996)
Lu, H., Pope, C. N., Townsend, P. K.
We examine $(D-2)$-brane solutions in supergravities, showing that they fall into four categories depending on the details of the dilaton coupling. In general they describe domain walls, although in...
Dyonic p-branes from self-dual (p+1)-branes (1996)
Green, M. B., Lambert, N. D., Papadopoulos, G., Townsend, P. K.
The `electromagnetic' $Sl(2;\bZ)$ duality group in spacetime dimension $D=4k$ can be given a Kaluza-Klein interpretation in $D=4k+2$ as the modular group of a compactifying torus. We show how dyonic...
Papadopoulos, G., Townsend, P. K.
We present the magnetic duals of G\"uven's electric-type solutions of D=11 supergravity preserving $1/4$ or $1/8$ of the D=11 supersymmetry. We interpret the electric solutions as $n$ orthogonal...
Duality of Type II 7-branes and 8-branes (1996)
Bergshoeff, E., De Roo, M., Green, M. B., Papadopoulos, G., Townsend, P. K.
We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing...
Duality of type-II 7-branes and 8-branes (1996)
Papadopoulos, G., Green, M.B., Roo, M. De, Bergshoeff, E., Townsend, P.K.
We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing...
The 2-brane and 4-brane solutions of ten dimensional IIA supergravity have a dual interpretation as Dirichlet-branes, or `D-branes', of type IIA superstring theory and as `M-branes' of an...
The IIA super-eightbrane (1995)
Bergshoeff, E., Green, M. B., Papadopoulos, G., Townsend, P. K.
We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing...
Supergravity solitons and non-perturbative superstrings (1995)
A review is given of the implications of supersymmetric black holes for the non-perturbative formulation of toroidally compactified superstrings, with particular emphasis on symmetry enhancement at...
Izquierdo, J. M., Lambert, N. D., Papadopoulos, G., Townsend, P. K.
We present dyonic multi-membrane solutions of the N=2 D=8 supergravity theory that serves as the effective field theory of the $T^2$-compactified type II superstring theory. The `electric' charge is...
The ten or eleven dimensional origin of central charges in the N=4 or N=8 supersymmetry algebra in four dimensions is reviewed: while some have a standard Kaluza-Klein interpretation as momenta in...
Compactification of D=11 supergravity on spaces of exceptional holonomy (1995)
Papadopoulos, G., Townsend, P. K.
We investigate the compactification of D=11 supergravity to D=5,4,3, on compact manifolds of holonomy $SU(3)$ (Calabi-Yau), $G_2$, and $Spin(7)$, respectively, making use of examples of the latter...
Anti-gravitating BPS monopoles and dyons (1995)
Gibbons, G. W., Townsend, P. K.
We show that the exact static, i.e. `anti-gravitating', magnetic multi monopole solutions of the Einstein/Maxwell/dilaton-YM/Higgs equations found by Kastor, London, Traschen, and the authors, for...
Enhanced Gauge Symmetries in Superstring Theories (1995)
Certain four-dimensional $N=4$ supersymmetric theories have special vacua in which massive charged vector supermultiplets become massless, resulting in an enhanced non-abelian gauge symmetry. We show...
New supergravities with central charges and Killing spinors in 2+1 dimensions (1995)
Howe, P. S., Izquierdo, J. M., Papadopoulos, G., Townsend, P. K.
We construct a new class of $(p,q)$-extended Poincar\'e supergravity theories in 2+1 dimensions as Chern-Simons theories of supersymmetry algebras with both central and automorphism charges. The new...
String-Membrane Duality in Seven Dimensions (1995)
The conjectured equivalence of the heterotic string to a $K_3$ compactified type IIA superstring is combined with the conjectured equivalence of the latter to a compactified 11-dimensional...
Supersymmetric spacetimes in 2+1 adS-supergravity models (1995)
Izquierdo, J. M., Townsend, P. K.
We find a class of (2+1)-dimensional spacetimes admitting Killing spinors appropriate to (2,0) adS-supergravity. The vacuum spacetimes include anti-de Sitter (adS) space and charged extreme black...
The eleven-dimensional supermembrane revisited (1995)
It is argued that the type IIA 10-dimensional superstring theory is actually a compactified 11-dimensional supermembrane theory in which the fundamental supermembrane is identified with the the...
Solitons in supersymmetric sigma-models with torsion (1995)
Papadopoulos, G., Townsend, P. K.
We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in...
Unity of Superstring Dualities (1994)
The effective action for type II string theory compactified on a six torus is $N=8$ supergravity, which is known to have an $E_{7}$ duality symmetry. We show that this is broken by quantum effects to...
Higher-dimensional resolution of dilatonic black hole singularities (1994)
Gibbons, G. W., Horowitz, Gary T., Townsend, P. K.
We show that the four-dimensional extreme dilaton black hole with dilaton coupling constant $a= \sqrt{p/(p+2)}$ can be interpreted as a {\it completely non-singular}, non-dilatonic, black $p$-brane...
Massive (p,q)-supersymmetric sigma models revisited (1994)
Papadopoulos, G., Townsend, P. K.
We recently obtained the conditions on the couplings of the general two-dimensional massive sigma-model required by (p,q)-supersymmetry. Here we compute the Poisson bracket algebra of the...
Macroscopic superstrings as interpolating solitons (1994)
Duff, M. J., Gibbons, G. W., Townsend, P. K.
It is known that, in string sigma-model metric, the `extreme' fivebrane solution of D=10 supergravity interpolates between D=10 Minkowski spacetime and a supersymmetric $S^3$ compactification to a...
Supersymmetric Self-Gravitating Solitons (1993)
Gibbons, G. W., Kastor, D., London, L. A. J., Townsend, P. K., Traschen, J.
We show that the `instantonic' soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs theory continue to be exact static, and stable,...
Massive sigma models with (p,q) supersymmetry (1993)
Papadopoulos, G., Townsend, P. K.
We determine the general scalar potential consistent with (p,q) supersymmetry in two-dimensional non-linear sigma models with torsion, generalizing previous results for special cases. We thereby find...
Vacuum interpolation in supergravity via super p-branes (1993)
Gibbons, G. W., Townsend, P. K.
We show that many of the recently proposed supersymmetric p-brane solutions of d=10 and d=11 supergravity have the property that they interpolate between Minkowski spacetime and a compactified...
Axionic Defect Anomalies and their Cancellation (1993)
Izquierdo, J. M., Townsend, P. K.
We present a simple derivation of the Callan-Harvey-Naculich effect, {\it i.e.} the compensation of charge violation on axion strings due to gauge anomalies by accretion of charge onto the string...
Potentials for (p,0) and (1,1) supersymmetric sigma models with torsion (1993)
Hull, C. M., Papadopoulos, G., Townsend, P. K.
Using (1,0) superfield methods, we determine the general scalar potential consistent with off-shell (p,0) supersymmetry and (1,1) supersymmetry in two-dimensional non-linear sigma models with...
Effective description of axion defects (1993)
Axion strings and domain walls exhibit a number of novel effects in the presence of gauge fields, in particular the electromagnetic field. It is shown how these effects are reproduced in a model of...
U(1)-extended gauge algebras in p-loop space (1993)
Townsend, P.K., Stelle, K.S., Sezgin, E., Percacci, R., Bergshoeff, E.
We consider, for p odd, a p-brane coupled to a (p + 1)th-rank background antisymmetric tensor field and to background Yang—Mills (YM) fields via a Wess—Zumino term. We obtain the generators of...
Low-Temperature Thermodynamics of $A^{(2)}_2$ and su(3)-invariant Spin Chains (1992)
Mezincescu, Luca, Nepomechie, Rafael I., Townsend, P. K., Tsvelik, A. M.
We formulate the thermodynamic Bethe Ansatz (TBA) equations for the closed (periodic boundary conditions) $A^{(2)}_2$ quantum spin chain in an external magnetic field, in the (noncritical) regime...
$U(1)$--Extended Gauge Algebras in $p$-Loop Space (1992)
Bergshoeff, E., Percacci, R., Sezgin, E., Stelle, K. S., Townsend, P. K.
We consider, for $p$ odd, a $p$--brane coupled to a $(p+1)$th rank background antisymmetric tensor field and to background Yang-Mills (YM) fields {\it via} a Wess-Zumino term. We obtain the...
Spacetime Scale-Invariance and the Super p-Brane (1992)
Bergshoeff, E., London, L. A. J, Townsend, P. K.
We generalize to p-dimensional extended objects and type II superstrings a recently proposed Green-Schwarz type I superstring action in which the tension $T$ emerges as an integration constant of the...
Spacetime scale-invariance and the super p-brane (1992)
Townsend, P.K., London, L.A.J., Bergshoeff, E.
We generalize to p-dimensional extended objects and type II superstrings a recently proposed Green-Schwarz type I superstring action in which the tension T emerges as an integration constant of the...
N = 2 superstrings in a supergravity background (1990)
Grisaru, Marc T, Howe, Paul S, Mezincescu, L, Nilsson, B, Townsend, P K
Super p-Branes as Gauge Theories of Volume Preserving Diffeomorphisms (1990)
Townsend, P.K., Tanii, Y., Sezgin, E., Bergshoeff, E.
We obtain the light-cone gauge-fixed action for a super p-brane. For p = 2 it is known that the action is equivalent to that of a one-dimensional super-Yang-Mills theory of the (infinite dimensional)...
Properties of the Eleven-Dimensional Supermembrane Theory (1988)
Townsend, P.K., Sezgin, E., Bergshoeff, E.
We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry...
On "spinning" membrane models (1988)
Townsend, P.K., Sezgin, E., Bergshoeff, E.
Several alternative actions for a bosonic membrane have recently been proposed. We show that a linearly realized locally world-volume-supersymmetric (spinning membrane) extension of any of these...
The Born-Infeld action from conformal invariance of the open superstring (1987)
Townsend, P.K., Pope, C.N., Sezgin, E., Bergshoeff, E.
We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of...
Supermembranes and eleven-dimensional supergravity (1987)
Townsend, P.K., Sezgin, E., Bergshoeff, E.
We construct an action for a supermembrane propagating in d=11 supergravity background. Using the constraints of d=11 curved superspace, we show that the action is invariant under Siegel-type...
Superstring actions in D = 3,4,6,10 curved superspace (1986)
Townsend, P.K., Sezgin, E., Bergshoeff, E.
The constraints on the supergeometry of D = 3,4,6,10 curved superspace, required for the coupling of supergravity to the Green-Schwarz superstring, are determined. We show that these are consistent...
Nicolai, Hermann, Townsend, P. K.
Ngreater-or-equal, slanted3 supergravity theories with vanishing one-loop trace anomaly may be constructed fron three basic N=3 multiplets, one of which contains an antisymmetric tensor gauge field....
Hidden constants: The θ parameter of QCD and the cosmological constant of N = 8 supergravity (1980)
Aurilia, A., Nicolai, Hermann, Townsend, P. K.
For field theories that include the abelian gauge field Aμνvarrho the field equations allow an arbitrary integration constant, which does not appear in the lagrangian but which does affect the...