Narrow Results

We explore a hidden possibility of BRST approach to higher spin field theory to obtain a consistent Lagrangian for massive spin- field in Einstein space of arbitrary d ≥ 3 dimension. Also, we prove that in the space under consideration the propagation of spin- field is hyperbolic and causal.

In this paper, we present the proof of a no-ghost theorem for the bosonic string in Nappi–Witten spacetime by the BRST-technology. The key point in this proof is to compare the characters with the signature functions, where traces are taken over the whole state space. It includes the states of Nappi–Witten string, the states of some extra unitary CFT and the conformal ghost states. Only the signature function of the Nappi–Witten string part is not trivial. Here we obtain it in a new complete basis for the states space of Nappi–Witten string. For all real number b, which is a parameter of the Nappi–Witten metric, the characters and the signature functions are exactly equivalent. Then we can state that the physical string states in Nappi–Witten group are all of non-negative norm.

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

In this paper, we will analyze the ABJM theory in harmonic superspace. The harmonic superspace variables will be parametrized by the coset SU(2)/U(1) and thus will have manifest supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical subspace from the total Hilbert space. We will also show that the evolution of the -matrix is unitary for this ABJM theory in harmonic superspace.

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed.

Witten's observables of topological Yang-Mills theory, defined as classes of an equivariant cohomology, are re-obtained as the BRST cohomology classes of a superspace version of the theory.

Using topological Yang–Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to find the most general solution to the problem of equivariant cohomology, and to recover the Donaldson–Witten polynomials when choosing a Wess–Zumino-type gauge.

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a $p$-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

After briefly describing Hamiltonian BRST methods and the multisymplectic approach to field theory, a symmetric geometric Lagrangian is studied by extending the BRST method to the multisymplectic setting. This work uses ideas first introduced by Hrabak [On the multisymplectic origin of the nonabelian deformation algebra of pseudoholomorphic embeddings in strictly almost Kähler ambient manifolds, and the corresponding BRST algebra, preprint (1999), arXiv: math-ph/9904026].

It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out, which yields a set of modified consistent anomalies.

A time-dependent strain induces non-Abelian gauge field in a sheet of graphene. We discuss the effective field theory of this system of graphene subjected to a general form of time-dependent strain. We study the modifications to this effective field theory as a result of breaking Lorentz symmetry down to its sub-group, $SIM(1)$, employing the VSR formalism. As the effective theory describing the graphene system has gauge symmetry; to quantize this theory, we add a suitable ghost and gauge fixing terms to the original action. The resultant action is observed to be invariant under a BRST symmetry. We have studied the BRST symmetry of the resultant theory, and explicitly constructed the BRST transformations.

A representation of general translation-invariant star products ⋆ in the algebra of $𝕄(ℂ)={lim}_{N\to \infty }{𝕄}_N(ℂ)$ is introduced which results in the Moyal–Weyl–Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so-called ⋆-cohomology, with groups $H_{\star }^k(ℂ)$, $k\ge 0$, is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achievements for the commutative fields, and is comparable to the Seiberg–Witten map for the Moyal case. Employing the Chern–Weil theory via the integral classes of $H_{\star }^k(\mathbb{Z})$ a noncommutative version of the Chern character is defined as an equivariant form which contains topological information about the corresponding translation-invariant noncommutative Yang–Mills theory. Thereby, we study the mentioned Yang–Mills theories with three types of actions of the gauge fields on the spinors, the ordinary, the inverse, and the adjoint action, and then some exact solutions for their anomalous behaviors are worked out via employing the homotopic correlation on the integral classes of ⋆-cohomology. Finally, the corresponding consistent anomalies are also derived from this topological Chern character in the ⋆-cohomology.