Gauge Invariant Action Research Articles

Duality invariance in massive theories

In this work, we show that duality symmetry can be implemented for massive theories at the level of the action, whenever we can formulate appropriate gauge invariant actions. For a massive vectorial field, we use a known gauge invariant description, while for a massive graviton, we introduce a novel gauge invariant action in order to show duality invariance.

Branes as solutions of gauge theories in gravitational field

The idea of the Gauss map is unified with the concept of branes as hypersurfaces embedded into $$D$$ -dimensional Minkowski space. The map introduces new generalized coordinates of branes alternative to their world vectors $$\mathbf {x}$$ and identified with the gauge and other massless fields. In these coordinates the Dirac $$p$$ -branes realize extremals of the Euler–Lagrange equations of motion of a $$(p+1)$$ -dimensional $$\mathrm{SO}(D-p-1)$$ gauge-invariant action in a gravitational background.

Gauge Theory on Twisted κ-Minkowski: Old Problems and Possible Solutions

We review the application of twist deformation formalism and the construction of noncommutative gauge theory on $\kappa$-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider ${U}(1)$ gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.

Minimal supergravity models of inflation

We present a superconformal master action for a class of supergravity models with one arbitrary function defining the Jordan frame. It leads to a gauge-invariant action for a real vector multiplet, which upon gauge fixing describes a massive vector multiplet, or to a dual formulation with a linear multiplet and a massive tensor field. In both cases the models have one real scalar, the inflaton, naturally suited for single-field inflation. Vectors and tensors required by supersymmetry to complement a single real scalar do not acquire vev's during inflation, so there is no need to stabilize the extra scalars which are always present in the theories with chiral matter multiplets. The new class of models can describe any inflaton potential which vanishes at its minimum and grows monotonically away from the minimum. In this class of supergravity models one can fit any desirable choice of inflationary parameters n_s and r.

Anomaly mediation from unbroken supergravity

When supergravity (SUGRA) is spontaneously broken, it is well known that anomaly mediation generates sparticle soft masses proportional to the gravitino mass. Recently, we showed that one-loop anomaly-mediated gaugino masses should be associated with unbroken supersymmetry (SUSY). This counterintuitive result arises because the underlying symmetry structure of (broken) SUGRA in flat space is in fact (unbroken) SUSY in anti-de Sitter (AdS) space. When quantum corrections are regulated in a way that preserves SUGRA, the underlying AdS curvature (proportional to the gravitino mass) necessarily appears in the regulated action, yielding soft masses without corresponding goldstino couplings. In this paper, we extend our analysis of anomaly mediation to sfermion soft masses. Already at tree-level we encounter a number of surprises, including the fact that zero soft masses correspond to broken (AdS) SUSY. At one-loop, we explain how anomaly mediation appears when regulating SUGRA in a way that preserves super-Weyl invariance. We find that recent claims in the literature about the non-existence of anomaly mediation were based on a Wilsonian effective action with residual gauge dependence, and the gauge-invariant 1PI effective action contains the expected anomaly-mediated spectrum. Finally, we calculate the sfermion spectrum to all orders, and use supertrace relations to derive the familiar two-loop soft masses from minimal anomaly mediation, as well as unfamiliar tree-level and one-loop goldstino couplings consistent with renormalization group invariance.

Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity

We review the Balitsky-Fadin-Kuraev-Lipatov approach to high-energy scattering in QCD and supersymmetric gauge theories. At a large number of colors, the equations for the gluon composite states in the t-channel have remarkable mathematical properties including their Mobius invariance, holomorphic separability, duality symmetry, and integrability. We formulate a theory of Reggeized gluon interactions in the form of a gauge-invariant effective action local in particle rapidities. In the maximally extended N=4 supersymmetry, the Pomeron is dual to the Reggeized graviton in the ten-dimensional anti-de Sitter space. As a result, the Gribov Pomeron calculus should be reformulated here as a generally covariant effective field theory for the Reggeized gravitons. We construct the corresponding effective action, which allows calculating the graviton Regge trajectory and its couplings. We sum the double-logarithmic contributions for amplitudes with graviton quantum numbers in the t-channel in the Einstein-Hilbert gravity and its supersymmetric generalizations. As the supergravity rank N increases, the double-logarithmic amplitudes begin to decrease rapidly compared with their Born contributions.

Extended Hamiltonian action for arbitrary spin fields in flat and AdS space

Totally symmetric, arbitrary spin massless and massive free fields in flat and AdS space and conformal fields in flat space are studied. An extended gauge-invariant Hamiltonian action for such fields is obtained. The action is constructed out of phase space fields and Lagrangian multipliers which are free of algebraic constraints. Gauge transformations of the phase space fields and Lagrangian multipliers are derived. Use of the Poincaré parametrization of AdS space allows us to treat fields in flat space and AdS space on an equal footing.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Gauge theory of topological phases of matter

We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a “gauge theory of states of matter” complementary to the well-known Landau theory of order parameters. We illustrate the power of our approach by deriving and interpreting the gauge-invariant effective actions of (topological) superconductors, 2D electron gases exhibiting the quantized Hall- and spin-Hall effect, 3D topological insulators, as well as axion electrodynamics. We also use the theory to elucidate the structure of surface modes in these systems.

Uniqueness of the gauge invariant action for cosmological perturbations

In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.

Parton-distribution functions for the pion and kaon in the gauge-invariant nonlocal chiral-quark model

We investigate the parton-distribution functions (PDFs) for the positively charged pion and kaon at a low-renormalization scale ~ 1 GeV. To this end, we employ the gauge-invariant effective chiral action from the nonlocal chiral-quark model, resulting in that the vector currents are conserved. All the model parameters are determined phenomenologically with the normalization condition for PDF and the empirical values for the pseudoscalar-meson weak-decay constants. We consider the momentum dependence of the effective quark mass properly within the model calculations. It turns out that the leading local contribution provides about 70 % of the total strength for PDF, whereas the nonlocal one that is newly taken into account in this work for the gauge invariance does the rest. High-Q^2 evolution to 27 GeV^2 is performed for valance-quark distribution function (VQDF), using the DGALP equation. The moments for the pion and kaon VQDFs are also computed. The numerical results are compared with the empirical data and theoretical estimations, and show qualitatively agreement with them.

Note on non-Abelian two-form gauge fields

Motivated by application to multiple M5-branes, we study some properties of non-Abelian two-form gauge theories. We emphasize that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a free theory or a topological system. We then propose a modification of transformation law which simplifies the gauge transformation of 3-form field strength and enables us to write down a gauge invariant action. We then argue that a generalization of Stueckelberg mechanism naturally gives mass to the two-form gauge field. For the application to multiple M5-branes, it should be identified with the KK modes.

INTERSECTION OF YANG–MILLS THEORY WITH GAUGE DESCRIPTION OF GENERAL RELATIVITY

An intersection of Yang–Mills theory with the gauge description of general relativity is considered. This intersection has its origin in a generalized algebra, where the generators of the SO(3, 1) group as gauge group of general relativity and the generators of a SU(N) group as gauge group of Yang–Mills theory are not separated anymore but are related by fulfilling nontrivial commutation relations with each other. Because of the Coleman–Mandula theorem this algebra cannot be postulated as Lie algebra. As consequence, extended gauge transformations as well as an extended expression for the field strength tensor is obtained, which contains a term consisting of products of the Yang–Mills connection and the connection of general relativity. Accordingly a new gauge invariant action incorporating the additional term of the generalized field strength tensor is built, which depends of course on the corresponding tensor determining the additional intersection commutation relations. This means that the theory describes a decisively modified interaction structure between the Yang–Mills gauge field and the gravitational field leading to a violation of the equivalence principle.

Obtaining gauge invariant actions via symplectic embedding formalism

AbstractThe concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.

Open superstring field theory I: gauge fixing, ghost structure, and propagator

The WZW form of open superstring field theory has linearized gauge invariances associated with the BRST operator Q and the zero mode eta_0 of the picture minus-one fermionic superconformal ghost. We discuss gauge fixing of the free theory in a simple class of gauges using the Faddeev-Popov method. We find that the world-sheet ghost number of ghost and antighost string fields ranges over all integers, except one, and at any fixed ghost number, only a finite number of picture numbers appear. We calculate the propagators in a variety of gauges and determine the field-antifield content and the free master action in the Batalin-Vilkovisky formalism. Unlike the case of bosonic string field theory, the resulting master action is not simply related to the original gauge-invariant action by relaxing the constraint on the ghost and picture numbers.

A spin-4 analog of 3D massive gravity

A sixth-order, but ghost-free, gauge-invariant action is found for a fourth-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity and is thus a spin-4 analog of linearized ‘new massive gravity’. Also found are ghost-free spin-4 analogs of linearized ‘topologically massive gravity’ and ‘new topologically massive gravity’, of fifth and eighth order, respectively.

Comments on lumps from RG flows

In this note we investigate the proposal of Ellwood and one of the authors et al. to construct a string field theory solution describing the endpoint of an RG flow from a reference BCFT to a target BCFT*. We show that the proposed class of solutions suffers from an anomaly in the equations of motion. Nevertheless, the gauge invariant action exactly reproduces the expected shift in energy.

Gauge invariance in braneworld scenarios

Rubakov and Shaposhnikov (RSH), in a seminal paper, discussed the possibility that particles are confined in a potential well. This is considered as the first mention to the todayʼs idea that we live in a brane, i.e., the braneworld concept. In this work we show precisely that the proposed RSH model has a gauge invariant equivalent action and we discuss it in the light of braneworld structure. We analyzed the intrinsic features of both models trying to disclose new properties within RSH braneworld theory.

Linearized interactions of scalar and vector fields with the higher spin field in AdS D

The explicit form of linearized gauge arid generalized “Weyl invariant” interactions of scalar and general higher even spin fields in the AdSD space constructed in [1] is reviewed. Also a linearized interaction of vector field with general higher even spin, gauge field is obtained. It is shown that the gauge invariant action of linearized vector field interacting with the higher spin field also includes the whole tower of invariant actions for couplings of the same vector field with the gauge fields of smaller even spin.

Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.