Antisymmetric Tensor Gauge Theory Research Articles

Non-BPS brane dynamics and dual tensor gauge theory

The action for the long wavelength oscillations of a non-BPS p=3 brane embedded in N=1, D=5 superspace is determined by means of the coset method. The D=4 world volume Nambu-Goldstone boson of broken translation invariance and the two D=4 world volume Weyl spinor Goldstinos of the completely broken supersymmetry describe the excitations of the brane into the broken space and superspace directions. The resulting action is an invariant synthesis of the Akulov-Volkov and Nambu-Goto actions. The D=4 antisymmetric tensor gauge theory action dual to the p=3 brane action is determined.

Bulk Kalb-Ramond field in the Randall-Sundrum scenario

We have considered the most general gauge invariant five-dimensional action of a second rank antisymmetric Kalb-Ramond tensor gauge theory, including a topological term of the form ${ϵ}^{ABLMN}{B}_{AB}{H}_{LMN}$ in a Randall-Sundrum scenario. Such a tensor field ${B}_{AB}$ (whose rank-3 field strength tensor is ${H}_{LMN}$), which appears in the massless sector of a heterotic string theory, is assumed to coexist with the gravity in the bulk. The third rank field strength corresponding to the Kalb-Ramond field has a well-known geometric interpretation as the space-time torsion. The only nontrivial classical solutions corresponding to the effective four-dimensional action are found to be self-dual or anti-self-dual Kalb-Ramond fields. This ensures that the four-dimensional effective action on the brane is parity-conserving. The massive modes for both cases, lying in the TeV range, are related to the fundamental parameters of the theory. These modes can be within the kinematic reach of forthcoming TeV-scale experiments. However, the couplings of the massless as well as massive Kalb-Ramond modes with matter on the visible brane are found to be suppressed vis-a-vis that of the graviton by the warp factor, whence the conclusion is that both the massless and the massive torsion modes appear much weaker than curvature to an observer on the visible brane.

QUANTIZATION OF MASSIVE ABELIAN ANTISYMMETRIC TENSOR FIELD AND LINEAR POTENTIAL

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is the same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.

Duality and confinement in massive antisymmetric tensor gauge theories

We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4 dimensions, to confinement of electric strings in the two dual models. The dual phase, in which magnetic strings are confined is absent. The presence of the confinement phase explicitly found in the 4-dimensional case, is generalized, using duality arguments, to arbitrary space-time dimensions.

Superspace gauge-invariant formulation of a massive tridimensional 2-form field

By dimensional reduction of a massive supersymmetric B$\wedge $F theory, a manifestly N=1 supersymmetric completion of a massive antisymmetric tensor gauge theory is constructed in (2+1) dimensions. In the N=1-D=3 superspace, a new topological term is used to give mass for the Kalb-Ramond field. We have introduced a massive gauge invariant model using the Stuckelberg formalism and an abelian topologically massive theory for the Kalb-Ramond superfield. An equivalence of both massive models is suggested. Further, a component field analysis is performed, showing a second supersymmetry in the model.

Non-abelian gravity and antisymmetric tensor gauge theory

A non-abelian generalisation of a theory of gravity coupled to a 2-form gauge field and a dilaton is found, in which the metric and 3-form field strength are Lie algebra-valued. In the abelian limit, the curvature with torsion is self-dual in four dimensions, or has SU( n) holonomy in 2 n dimensions. The coupling to self-dual Yang-Mills fields in 4 dimensions, or their higher dimensional generalisation, is discussed. The abelian theory is the effective action for (2,1) strings, and the non-abelian generalisation is relevant to the study of coincident branes in the (2,1) string approach to M-theory. The theory is local when expressed in terms of a vector prepotential.

Exotic solutions in Einstein-antisymmetric tensor theory

Classical solutions of the self-interacting, non-abelian antisymmetric tensor gauge theory of Freedman and Townsend coupled to Einstein gravity are discussed. Particularly, it is demonstrated that the theory admits a classical metric solution which, depending on the value of the gauge coupling parameter of the theory, exhibits a black hole with an exotic non-abelian hair or a spacetime showing the “violation of the cosmic censorship hypothesis” which should be distinguished from white holes.

Bosonization of Thirring Model in Arbitary Dimension

We propose to use a novel master Lagrangian for performing the bosonization of the $D$-dimensional massive Thirring model in $D=d+1 \ge 2$ dimensions. It is shown that our master Lagrangian is able to relate the previous interpolating Lagrangians each other which have been recently used to show the equivalence of the massive Thirring model in (2+1) dimensions with the Maxwell-Chern-Simons theory. Starting from the phase-space path integral representation of the master Lagrangian, we give an alternative proof for this equivalence up to the next-to-leading order in the expansion of the inverse fermion mass. Moreover, in (3+1)-dimensional case, the bosonized theory is shown to be equivalent to the massive antisymmetric tensor gauge theory. As a byproduct, we reproduce the well-known result on bosonization of the (1+1)-dimensional Thirring model following the same strategy. Finally a possibility of extending our strategy to the non-Abelian case is also discussed.

Volume-preserving diffeomorphisms' versus local gauge symmetry

We present a new form of quantum electrodynamics where the photons are composites made out of zero-dimensional scalar “primitives”. The role of the local gauge symmetry is taken over by an infinite-dimensional global Noether symmetry - the group of volume-preserving (symplectic) diffeomorphisms of the target space of the scalar primitives. A similar construction can be carried out for higher antisymmetric tensor gauge theories. Solutions of the Maxwell equations are automatically solutions of the new system. However, the latter possesses additional non-Maxwell solutions which display some interesting new effects: (a) a magneto-hydrodynamical analogy, (b) absence of the electromagnetic self-energy for electron plane wave solutions, and (c) gauge invariant photon mass generation, where the magnitude of the generated mass is arbitrary.

Antisymmetric-tensor gauge theory and polynomial invariants of links

Non-abelian (topological) gauge theory of antisymmetric tensor field, so-calledBF-theory, is analysed from the point of view of its applications to description of topological invariants of higher-dimensional links. Topological matter multiplets, playing the role of physical observables, are introduced to measure linking phenomena in the target space of arbitrary dimension. The whole theory, as a highly on-shell reducible gauge system, is quantized in the framework of the formalism of Batalin and Vilkovisky. A monodromy matrix, giving rise to a skein relation, is derived in a manifestly covariant path-integral way. A relationship with quantum groups is also mentioned.

OFF-SHELL NILPOTENCY FOR ON-SHELL REDUCIBILITY

The direct way of Lagrangian BRS gauge-fixing we proposed recently is applied to reducible gauge theories; antisymmetric tensor gauge theories are considered as definite examples. It enables us to do without ad hoc ghosts for ghosts. It also achieves BRS-exact forms of full gauge-fixing terms by means of off-shell nilpotent BRS transformations.

BRS structure of the antisymmetric tensor gauge theories

We analyze the BRS structure and display the quantum effective lagrangian for two models: the antisymmetric 2-tensor non-abelian field coupled to a Yang-Mills field and the free antisymmetric tensor of arbitrary rank in arbitrary dimension.

Super p-branes as gauge theories of volume preserving diffeomorphisms

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) area preserving diffeomorphism group of the membrane. We show that for p > 2 the action is that of a new kind of supersymmetric gauge theory of p-volume-preserving diffeomorphisms that is not of Yang-Mills type, and we conjecture that it is related to an infinite-dimensional non-Abelian antisymmetric tensor gauge theory. We compute the classical algebra of the supersymmetry charges and generators of the volume preserving diffeomorphisms, and show that it does not allow central extensions.

SP(2)–BRST quantization of the antisymmetric tensor gauge theory

A general method is given for the construction of gauge-fixed BRS and anti-BRS invariant action for the antisymmetric tensor gauge theory. The method is based on the single requirement that the space of fields carries an irreducible representation of the SP(2)–BRST algebra.

Hamiltonian BRST quantization of antisymmetric tensor gauge theory

Following the systematic hamiltonian BRST quantization procedure we study the quantization of a non-abelian antisymmetric tensor gauge theory. After discussing the gauge symmetry of the theory we construct the nilpotent BRST charge Q and find out the form of the quantum, gauge-fixed action which describes the unitary theory. The transition to the configuration space yields the covariant lagrangian action containing a three-ghost coupling, with Q 2 = 0 on shell.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

Generalized canonical quantization of antisymmetric tensor gauge theory

The gauge-fixing problem in the nonabelian antisymmetric tensor gauge theory is discussed by using the systematic hamiltonian BRST approach. The BRST symmetry of the quantum action is defined with an off-shell nilpotent BRST charge, which insures unitarity. The transition to the covariant lagrangian description, containing a trilinear ghost coupling, is obtained.

Anti-symmetric tensor gauge theories

Anti-symmetric tensor gauge theories are quantized via the Faddeev-Popov procedure leading to a BRS invariant theory without the need for second order ghosts. The quantum mechanical equivalence of these theories to non-linear sigma models is established using the spontaneously broken global symmetry currents. Upon gauging these symmetries the Higgs mechanism is displayed, while for anomalous symmetries an analog of the Wess-Zumino action is constructed in terms of the anti-symmetric tensor gauge fields.

Lagrangian and Hamiltonian BRST structures of the antisymmetric tensor gauge theory.

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Witten's string field theory.

Quantization and unitary in antisymmetric tensor gauge theories

Abstract Following the procedure of Batalin and Vilkovisky we discuss the quantization of a non-abelian antisymmetric tensor gauge theory and describe the verification of one-loop unitarity for the quantized model, using the Ward identities and the procedure of 't Hooft and Veltman. The quantization of this system is similar to that of the Witten string field theory, requiring among other things the presence of three-ghost couplings.