Searcharxiv⌕ Search

arXiv subjects

Friedemann Brandt

Publications and source records attributed to Friedemann Brandt.

52 records · Page 3Linked to original sources
arXiv1997

Extended antifield-formalism

The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation laws, associated with conserved antisymmetric tensors. Otherwise, one may encounter obstructions of the type discussed in [13]. These higher order conservation laws are shown to define additional rigid symmetries of the master equation and to form -- together with the standard symmetries -- an interesting algebraic structure. They lead furthermore to independent Ward identities which are derived in the standard manner, because the resulting master ("Zinn-Justin") equation capturing both the gauge symmetries and the rigid symmetries of all orders takes a known form. Issues such as anomalies or consistent deformations of the action preserving some set of rigid symmetries can be also systematically analysed in this framework.

hep-th↗
arXiv1997

Local BRST cohomology and covariance

The paper provides a framework for a systematic analysis of the local BRST cohomology in a large class of gauge theories. The approach is based on the cohomology of s+d in the jet space of fields and antifields, s and d being the BRST operator and exterior derivative respectively. It relates the BRST cohomology to an underlying gauge covariant algebra and reduces its computation to a compactly formulated problem involving only suitably defined generalized connections and tensor fields. The latter are shown to provide the building blocks of physically relevant quantities such as gauge invariant actions, Noether currents and gauge anomalies, as well as of the equations of motion.

hep-th↗
arXiv1997

The rigid symmetries of bosonic D-strings

We analyse the classical symmetries of bosonic D-string actions and generalizations thereof. Among others, we show that the simplest actions of this type have infinitely many nontrivial rigid symmetries which act nontrivially and nonlinearly both on the target space coordinates and on the U(1) gauge field, and form a Kac-Moody version of the Weyl algebra (= Poincare algebra + dilatations).

hep-th↗
arXiv1997

Deformed supergravity with local R-symmetry

Using deformation theory based on BRST cohomology, a supergravity model is constructed which interpolates through a continuous deformation parameter between new minimal supergravity with an extra U(1) gauge multiplet and standard supergravity with local R-symmetry in a formulation with a nonstandard set of auxiliary fields. The deformation implements an electromagnetic duality relating the extra U(1) to the R-symmetry. A consistent representative of the R-anomaly in the model is proposed too.

hep-th↗
arXiv1996

On the determination of anomalies in supersymmetric theories

We develop an efficient technique to compute anomalies in supersymmetric theories by combining the so-called nonlocal regularization method and superspace techniques. To illustrate the method we apply it to a four dimensional toy model with potentially anomalous N=1 supersymmetry and prove explicitly that in this model all the candidate supersymmetry anomalies have vanishing coefficients at the one-loop level.

hep-th↗
arXiv1996

Ward identities for rigid symmetries of higher order

Higher order conservation laws, associated with conserved antisymmetric tensors $j^{μ_1 ... μ_k}$ fulfilling $\partial_{μ_1} j^{μ_1 ... μ_k} \approx 0$, are shown to define rigid symmetries of the master equation. They thus lead to independent Ward identities which are explicitly derived.

hep-th↗
arXiv1996

Global Symmetries in the Antifield-Formalism

In this paper, two things are done. (i) First, it is shown that any global symmetry of a gauge-invariant theory can be extended to the ghosts and the antifields so as to leave invariant the solution of the master-equation (before gauge fixing). (ii) Second, it is proved that the incorporation of the rigid symmetries to the solution of the master-equation through the introduction of a constant ghost for each global symmetry can be obstructed already at the classical level whenever the theory possesses higher order conservation laws. Explicit examples are given.

hep-th↗
arXiv1996

The BRST--antibracket cohomology of $2d$ gravity conformally coupled to scalar matter

We compute completely the BRST--antibracket cohomology on local functionals in two-dimensional Weyl invariant gravity for given classical field content (two dimensional metric and scalar matter fields) and gauge symmetries (two dimensional diffeomorphisms and local Weyl transformations). This covers the determination of all classical actions, of all their rigid symmetries, of all background charges and of all candidate gauge anomalies. In particular we show that the antifield dependence can be entirely removed from the anomalies and that, if the target space has isometries, the condition for the absence of matter field dependent Weyl anomalies is more general than the familiar `dilaton equations'.

hep-th↗
arXiv1996

Background charges and consistent continuous deformations of $2d$ gravity theories

We construct and discuss all background charges and continuous consistent deformations of standard $2d$ gravity theories with scalar matter fields. It turns out that the background charges and those deformations which change nontrivially both the form of the action and of its gauge symmetries are closely linked and exist only if the target space has at least one special (`covariantly constant') Killing vector which must be a null vector in the case of the deformations. The deformed actions provide interesting novel $2d$ gravity models. We argue that some of them lead to non-critical string theories.

hep-th↗
arXiv1995

Local BRST cohomology in Einstein--Yang--Mills theory

We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general diffeomorphism and gauge invariant actions. The analysis is carried out in all spacetime dimensions larger than 2 and for all ghost numbers. This covers the classification of all candidate anomalies, of all consistent deformations of the action, as well as the computation of the (equivariant) characteristic cohomology, i.e. the cohomology of the spacetime exterior derivative in the space of (gauge invariant) local differential forms modulo forms that vanish on-shell. We show in particular that for a semi-simple Yang-Mills gauge group the antifield dependence can be entirely removed both from the consistent deformations of the Lagrangian and from the candidate anomalies. Thus, the allowed deformations of the action necessarily preserve the gauge structure, while the only candidate anomalies are those provided by previous works not dealing with antifields, and by ``topological" candidate anomalies which are present only in special spacetime dimensions (6,9,10,13,...). This result no longer holds in presence of abelian factors where new candidate anomalies and deformations of the action can be constructed out of the conserved Noether currents (if any). The Noether currents themselves are shown to be covariantizable, with a few exceptions discussed as well.

hep-th↗
arXiv1995

Conserved currents and gauge invariance in Yang-Mills theory

It is shown that in the absence of free abelian gauge fields, the conserved currents of (classical) Yang-Mills gauge models coupled to matter fields can be always redefined so as to be gauge invariant. This is a direct consequence of the general analysis of the Wess-Zumino consistency condition for Yang-Mills theory that we have provided recently.

hep-th↗
arXiv1994

BRST-Antibracket Cohomology in 2D Conformal Gravity

We present results of a computation of the BRST-antibracket cohomology in the space of local functionals of the fields and antifields for a class of 2d gravitational theories which are conformally invariant at the classical level. In particular all classical local action functionals, all candidate anomalies and all BRST--invariant functionals depending nontrivially on antifields are given and discussed for these models.

hep-th↗
arXiv1994

Bäcklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations

It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.

hep-th↗
arXiv1993

Structure of BRS-Invariant Local Functionals

For a large class of gauge theories a nilpotent BRS-operator $s$ is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of $\4s=s+d$ on functions $f(\4C,\PH)$ of tensor fields $\PH$ and of variables $\4C$ which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly candidates whose BRS-variation vanishes off-shell. The assumptions under which the result holds are thoroughly discussed.

hep-th↗
arXiv1993

Anomaly candidates and invariants of D=4, N=1 supergravity theories

All anomaly candidates and the form of the most general invariant local action are given for old and new minimal supergravity, including the cases where additional Yang--Mills and chiral matter multiplets are present. Furthermore nonminimal supergravity is discussed. In this case local supersymmetry itself may be anomalous and some of the corresponding anomaly candidates are given explicitly. The results are obtained by solving the descent equations which contain the consistency equation satisfied by integrands of anomalies and invariant actions.

hep-th↗