Searcharxiv⌕ Search

arXiv subjects

Friedemann Brandt

Publications and source records attributed to Friedemann Brandt.

At least 19 recordsLinked to original sources
arXiv2023

4D supersymmetric gauge theories of spacetime translations

The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local spacetime translations and supersymmetries generated by transformations whose commutators contain infinitesimal local spacetime translations. It is shown that, up to local field redefinitions, there is a unique class of such supersymmetric field theories satisfying specified prerequisites which particularly concern the field content of the theories. The theories of this class have global supersymmetry and are similar to globally supersymmetric Yang-Mills theories.

hep-th↗
arXiv2021

Comment on "A Candidate for a Supergravity Anomaly"

In a recent paper (arXiv:2110.06213v1) it was argued that in 4D supergravity a previously unknown candidate anomaly exists. In the present paper it is pointed out that the existence of such a candidate would contradict results available in the literature, and it is substantiated that there is no candidate anomaly of the asserted form.

hep-th↗
arXiv2021

Properties of an alternative off-shell formulation of 4D supergravity

This article elaborates on an off-shell formulation of D=4, N=1 supergravity whose auxiliary fields comprise an antisymmetric tensor field without gauge degrees of freedom. In particular, the relation to new minimal supergravity, a supercovariant tensor calculus and the construction of invariant actions including matter fields are discussed.

hep-th↗
arXiv2020

Consistent interactions of Curtright fields

Consistent self-interactions of Curtright fields (Lorentz tensors with (2,1) Young diagram index symmetry) are constructed in dimensions 5 and 7. Most of them modify the gauge transformations of the free theory but the commutator algebra of the deformed gauge transformations remains Abelian in all cases. All of these interactions contain terms cubic in the Curtright fields with four or five derivatives, which are reminiscent of Yang-Mills, Chapline-Manton, Freedman-Townsend and Chern-Simons interactions, respectively.

hep-th↗
arXiv2017

Counterpart of the Weyl tensor for Rarita-Schwinger type fields

In dimensions larger than 3 a modified field strength for Rarita-Schwinger type fields is constructed whose components are not constrained by the field equations. In supergravity theories the result provides a modified (supercovariant) gravitino field strength related by supersymmetry to the (supercovariantized) Weyl tensor. In various cases, such as for free Rarita-Schwinger type gauge fields and for gravitino fields in several supergravity theories, the modified field strength coincides on-shell with the usual field strength. A corresponding result for first order derivatives of Dirac type spinor fields is also presented.

hep-th↗
arXiv2013

Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11

The primitive elements of the supersymmetry algebra cohomology as defined in previous work are derived for standard supersymmetry algebras in dimensions D=5,...,11 for all signatures of the related Clifford algebras of gamma matrices and all numbers of supersymmetries. The results are presented in a uniform notation along with results of previous work for D=4, and derived by means of dimensional extension from D=4 up to D=11.

hep-th↗
arXiv2012

BRST Symmetry and Cohomology

We present the mathematical considerations which determine all gauge invariant actions and anomaly candidates in gauge theories of standard type such as ordinary or gravitational Yang Mills theories. Starting from elementary concepts of field theory the discussion tries to be explicit and complete, only the cohomology of simple Lie algebras it quoted from the literature.

hep-th↗
arXiv2012

Aspects of supersymmetric BRST cohomology

The application and extension of well-known BRST cohomological methods to supersymmetric field theories are discussed. The focus is on the emergence and particular features of supersymmetry algebra cohomology in this context. In particular it is discussed and demonstrated that supersymmetry algebra cohomology emerges within the cohomological analysis of standard supersymmetric field theories whether or not the commutator algebra of the symmetry transformations closes off-shell.

hep-th↗
arXiv2010

Supersymmetry algebra cohomology I: Definition and general structure

The paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra cohomology, and corresponding "primitive elements" are defined by means of a BRST-type coboundary operator. A method to systematically compute this cohomology is outlined and illustrated by simple examples.

hep-th↗
arXiv2010

Lectures on supergravity

The text is an essentially self-contained introduction to four-dimensional N=1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general relativity. Emphasis is put on showing how supergravity fits in the general framework of gauge theories and how it can be derived from a tensor calculus for gauge theories of a standard form. Contents: 1. Introduction, 2. Gauge symmetries in the jet space approach, 3. D=4, N=1 pure supergravity, 4. Tensor calculus for standard gauge theories, 5. Off-shell formulations of D=4, N=1 supergravity with matter, A. Lorentz algebra, spinors, Grassmann parity, B. Explicit verification of local supersymmetry.

hep-th↗
arXiv2003

Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory

We analyze in detail the recursive construction of the Seiberg-Witten map and give an exhaustive description of its ambiguities. The local BRST cohomology for noncommutative Yang-Mills theory is investigated in the framework of the effective commutative Yang-Mills type theory. In particular, we show how some of the conformal symmetries get obstructed by the noncommutative deformation.

hep-th↗
arXiv2003

Anomaly freedom in Seiberg-Witten noncommutative gauge theories

We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the $ε^{\m_1\m_2\m_3\m_4}$ part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter $θ^{\m\n}$. And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.

hep-th↗
arXiv2003

Asymptotically anti-de Sitter space-times: symmetries and conservation laws revisited

In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat metric induced on the boundary. The fall-off conditions for the metric perturbations that guarantee finiteness of the associated conserved charges are derived.

gr-qc↗
arXiv2003

Extended BRST cohomology, consistent deformations and anomalies of four-dimensional supersymmetric gauge theories

The local cohomology of an extended BRST differential which includes global N=1 supersymmetry and Poincare transformations is completely and explicitly computed in four-dimensional supersymmetric gauge theories with super-Yang-Mills multiplets, chiral matter multiplets and linear multiplets containing 2-form gauge potentials. In particular we determine to first order all N=1 supersymmetric and Poincare invariant consistent deformations of these theories that preserve the N=1 supersymmetry algebra on-shell modulo gauge transformations, and all Poincare invariant candidate gauge and supersymmetry anomalies. When the Yang-Mills gauge group is semisimple and no linear multiplets are present, we find that all such deformations can be constructed from standard superspace integrals and preserve the supersymmetry transformations in a formulation with auxiliary fields, and the candidate anomalies are exhausted by supersymmetric generalizations of the well-known chiral anomalies. In the general case there are additional deformations and candidate anomalies which are relevant especially to the deformation of free theories and the general classification of interaction terms in supersymmetric field theories.

hep-th↗
arXiv2002

Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the construction which originate from the freedom in the Seiberg-Witten map are discussed with regard to the question whether they can lead to inequivalent models, i.e., models not related by field redefinitions.

hep-th↗