BRST Symmetry Research Articles

Symplectic gauge-invariant reformulation of a free-particle system on toric geometry

We deduce the constraint structure and subsequently quantize a free-particle system residing on a torus satisfying the geometric constraint , within the framework of the modified Faddeev-Jackiw formalism. Further, we reformulate the system as a gauge theory by means of the symplectic gauge-invariant formalism. Finally, we establish the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries of the reformulated gauge-invariant theory.

General cubic interacting vertex for massless integer higher spin fields

We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities s1,s2,s3. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [14] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.

BRST analysis and BFV quantization of the generalized quantum rigid rotor

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the [Formula: see text] nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

Matrix integrals & finite holography

We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

Twisted BRST symmetry in gauge theories on the κ -Minkowski spacetime

Algebraic properties of the BRST symmetry associated to the twisted gauge symmetry occurring in the $\kappa$-Poincar\'e invariant gauge theories on the $\kappa$-Minkowski space are investigated. We find that the BRST operation associated to the gauge invariance of the action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent twisted BRST operation, leading to a twisted BRST symmetry algebra which may be viewed as a noncommutative analog of the usual Yang-Mills BRST algebra.

A canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics in first-order formalism

We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

Nakanishi–Kugo–Ojima quantization of general relativity in Heisenberg picture

The Chern–Weil topological theory is applied to a classical formulation of general relativity in four-dimensional spacetime. Einstein–Hilbert gravitational action is shown to be invariant with respect to a novel translation (co-translation) operator up to the total derivative; thus, a topological invariant of a second Chern class exists owing to Chern–Weil theory. Using topological insight, fundamental forms can be introduced as a principal bundle of the spacetime manifold. Canonical quantization of general relativity is performed in a Heisenberg picture using the Nakanishi–Kugo–Ojima formalism in which a complete set of quantum Lagrangian and BRST transformations including auxiliary and ghost fields is provided in a self-consistent manner. An appropriate Hilbert space and physical states are introduced into the theory, and the positivity of these physical states and the unitarity of the transition matrix are ensured according to the Kugo–Ojima theorem. The nonrenormalizability of quantum gravity is reconsidered under the formulation proposed herein.

Soft-collinear effective theory: BRST formulation

We provide a BRST formalism for the soft-collinear effective theory describing interactions of soft and collinear degrees of freedom in the presence of a hard interaction. In particular, we develop a BRST symmetry transformation for SCET theory. We further generalize the BRST formulation by making the transformation parameter field dependent. This establishes a mapping between several SCET actions consistently when defined in different gauge conditions. In fact, a definite structure of gauge-fixed actions corresponding to any particular gauge condition can be generated for SCET theory using our formulation.

Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius R=sqrt{pp^{prime }} has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT-symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2, p) minimal string as suggested by Seiberg and Stanford.

Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $$M_{23}$$

Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of square-free level. These belong to a larger class of Borcherds-Kac-Moody (super)algebras Borcherds obtained by twisting the denominator identity of the Fake Monster Lie algebra. Borcherds asked whether these Lie (super)algebras admit natural constructions. For the ten Lie algebras from the classification we give a positive answer to this question, i.e. we prove that they can be realised uniformly as the BRST cohomology of suitable vertex algebras.

Frac{mathrm{SL}left(2,mathrm{mathbb{R}}right)times mathrm{U}(1)}{mathrm{U}(1)} CFT, NS5+F1 system and single trace Toverline{T}

In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model frac{mathrm{SL}{left(2,mathrm{mathbb{R}}right)}_ktimes mathrm{U}(1)}{mathrm{U}(1)} × S3 × T4 with SL(2, ℝ) WZW level k ≥ 2, (ii) the full near horizon theory of the NS5 branes with k NS5 branes wrapping T4 × S1, p » 1 F1 strings wrapping S1 and n units of momentum along the S1 and (iii) the single trace Toverline{T} deformation of string theory in AdS3 × S3 × T4. As a check we compute the spectrum (continuous) of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace Toverline{T} deformed string theory in AdS3. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach.

Single extra dimension from \u03ba-Poincar\xe9 and gauge invariance

We show that κ-Poincaré invariant gauge theories on κ-Minkowski space with physically acceptable commutative (low energy) limit must be 5-d. The gauge invariance requirement of the action fixes the dimension of the κ-Minkowski space to d = 5 and selects the unique twisted differential calculus with which the construction can be achieved. We characterize a BRST symmetry related to the 5-d noncommutative gauge invariance though the definition of a nilpotent operation, which is used to construct a gauge-fixed action. We also consider standard scenarios assuming (compactification of) flat extra dimension, for which the 5-d deformation parameter κ can be viewed as the bulk 5-d Planck mass. We study physical properties of the resulting 4-d effective theories. Recent data from collider experiments require κ ≳ mathcal{O} (1013) GeV. The use of standard test of in-vacuo dispersion relations of Gamma Ray Burst photons increases this lower bound by 4 orders of magnitude. The robustness of this bound is discussed in the light of possible new features of noncommutative causal structures.

A note on gauge anomaly cancellation in effective field theories

The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

BRST-BV quantum actions for constrained totally-symmetric integer HS fields

A constrained BRST–BV Lagrangian formulation for totally symmetric massless HS fields in a d-dimensional Minkowski space is extended to a non-minimal constrained BRST–BV Lagrangian formulation by using a non-minimal BRST operator Qc|tot with non-minimal Hamiltonian BFV oscillators C‾,P‾,λ,π, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion ΨH as a kernel of the gauge-fixing BRST–BV Fermion functional Ψ, manifesting the concept of BFV–BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion Ψ in a total BRST–BV action S0|sΨ=∫dη0〈χtot|cΨ0|Qc|tot|χtot|cΨ0〉. We use a gauge condition which depends on two gauge parameters, thereby extending the case of Rξ-gauges. For triplet and doublet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Green's functions, BRST symmetry transformations are suggested and Ward identities are obtained.

On quantum obstruction spaces and higher codimension gauge theories

Using the quantum construction of the BV-BFV method for perturbative gauge theories, we show that the obstruction for quantizing a codimension 1 theory is given by the second cohomology group with respect to the boundary BRST charge. Moreover, we give an idea for the algebraic construction of codimension k quantizations in terms of Ek-algebras and higher shifted Poisson structures by formulating a higher version of the quantum master equation.

The chiral algebra of genus two class mathcal{S} theory

We construct the chiral algebra associated with the A1-type class mathcal{S} theory for the genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we find a set of chiral algebra generators that form closed OPEs. Given the fact that they reproduce the spectrum of chiral algebra operators up to large dimensions, we conjecture that they are the complete set of generators. Remarkably, their OPEs are invariant under an action of SU(2) which is not associated with any conserved one-form current in four dimensions. We find that this novel SU(2) strongly constrains the OPEs of non-scalar Schur operators. For completeness, we also check the equivalence of Schur indices computed in two S-dual descriptions with a non-vanishing flavor fugacity turned on.

Quantization of non-Abelian gauge theory in graphene

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, [Formula: see text], 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 Model of Boson in (1 + 1) Dimension with the Non-Covariant Masslike Term for the Gauge Field

We consider the gauged model of Siegel type chiral boson with a Lorentz non-covariant mass-like term for the gauge fields which is found to be equivalent to a model of boson where the kinetic term is like the kinetic term of Floreanini-Jackiw type chiral boson. We carry out the quantization of gauge non-invariant version this model in both the Lagrangian and Hamiltonian formulation. The quantization of the gauge-invariant version of this model in the extended phase space also has been carried out in the Lagrangian formulation. The gauge-invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition. BRST symmetry associated with this model has been studied with different gauge fixing terms. It has been shown that the same model shows off-shell as well as on-shell BRST invariance depending on the choice of gauge fixing term.

Hamiltonian BRST-invariant deformations in Abelian gauge theory with higher derivative matter fields

We construct the consistent interactions among the Abelian gauge fields and various higher derivative matter fields within the framework of the Hamiltonian BRST formalism. To achieve this, we mainly investigate a set of iterative equations with respect to the free model under study by using the cohomological technique. Concretely, it is shown that the second-order and the other higher-order deformations of the BRST charge are supposed to be zero. While for the BRST-invariant Hamiltonian, the third-order as well as the corresponding higher-order deformation terms vanish completely for scalar fields. In special, the deformation of BRST-invariant Hamiltonian for the spinor field model terminates at order one as we can imagine. Furthermore, after plugging these deformed quantities into the original Hamiltonian and exploiting the ghost-independent terms, we recover the usual local gauge symmetries of the resulting interacting theory which can be interpreted as the gaugings of the rigid invariance of the uncoupled system.

A modification of Faddeev–Popov approach free from Gribov ambiguity

We propose a modified version of the Faddeev–Popov (FP) quantization approach for non-Abelian gauge field theory to avoid Gribov ambiguity. We show that by means of introducing a new method of inserting the correct identity into the Yang–Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of Gribov ambiguity can be removed naturally. Meanwhile by handling the absolute value of the FP determinant with the method introduced by Williams and collaborators, we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian. The new Lagrangian will have a nilpotent symmetry which can be viewed as an analog of the Becchi–Rouet–Stora–Tyutin symmetry.