Off-shell Effective Action Research Articles

Stability of the de-Sitter universe: one-loop nonlocal f (R) gravity

With the method of the background field expansion, we investigate the one-loop quantization of the Euclidean nonlocal f (R) model in the de-Sitter universe. We obtain the ghost-free condition (GFC) based on the transformation from the Jordan frame to the Einstein frame and the classical stability condition (CSC) satisfied \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{RR}^{\\left(0\\right)}-{\\phi }_{0}{F}_{RR}^{\\left(0\\right)}<0$$\\end{document}. We present the on-shell and off-shell one-loop effective action and quantum stability condition (QSC) by utilizing the generalized zeta-function. We find that under the fulfillment of GFC, CSC and QSC are inconsistent.

On two-loop divergences of effective action in 6D, mathcal{N} = (1, 1) SYM theory

We study the off-shell structure of the two-loop effective action in 6D, mathcal{N} = (1, 1) supersymmetric gauge theories formulated in mathcal{N} = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D, mathcal{N} = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest mathcal{N} = (1, 0) supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of frac{1}{varepsilon^2} and demonstrate that the corresponding expressions are non-local in harmonics.

Entropy functional and the holographic attractor mechanism

We provide a field theory interpretation of the attractor mechanism for asymptotically AdS4 dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.

Asymptotic safety goes on shell

It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein–Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.

Anomalous U(1) models in four and five dimensions and their anomaly poles

We analyze the role played by anomaly poles in an anomalous gauge theory by discussing their signature in the corresponding off-shell effective action. The origin of these contributions, in the most general kinematical case, is elucidated by performing a complete analysis of the anomaly vertex at perturbative level. We use two independent (but equivalent) representations: the Rosenberg representation and the longitudinal/transverse (L/T) parameterization, used in recent studies of g−2 of the muon and in the proof of non-renormalization theorems of the anomaly vertex. The poles extracted from the L/T parameterization do not couple in the infrared for generic anomalous vertices, as in Rosenberg, but we show that they are responsible for the violations of unitarity in the UV region, using a class of pole-dominated amplitudes. We conclude that consistent formulations of anomalous models require necessarily the cancellation of these polar contributions. Establishing the UV significance of these terms provides a natural bridge between the anomalous effective action and its completion by a nonlocal theory. Some additional difficulties with unitarity of the mechanism of inflow in extra dimensional models with an anomalous theory on the brane, due to the presence of anomaly poles, are also pointed out.

2PI effective action and gauge dependence identities

The problem of maintaining gauge invariance when truncating the two particle irreducible (2PI) effective action has been studied recently by several authors. Here we give a simple and very general derivation of the gauge dependence identities for the off-shell 2PI effective action. We consider the case where the gauge is fixed by an arbitrary function of the quantum gauge field, subject only to the restriction that the Faddeev-Popov matrix is invertable. We also study the background field gauge. We address the role that these identies play in solving gauge invariance problems associated with physical quantities calculated using a truncated on-shell 2PI effective action.

Power of supersymmetry in D-particle dynamics

A new systematic method is developed to study to what extent the symmetry requirements alone, above all the invariance under 16 supersymmetries (SUSY), determine the completely off-shell effective action Γ of a D-particle, i.e., without imposing any restrictions on its position r m ( τ) and spin θ α ( τ). Our method consists of (i) writing down the proper closure relations for general SUSY transformations δ ϵ (which necessarily involves Γ itself) together with the invariance condition δ ϵ Γ=0 (ii) and solving this coupled system of functional differential equations for δ ϵ and Γ simultaneously, modulo field redefinitions, in a consistent derivative expansion scheme. Our analysis is facilitated by a novel classification scheme introduced for the terms in Γ. At order 2 and 4, although no assumption is made on the underlying theory, we reproduce the effective action previously obtained at the tree and the 1-loop level in Matrix theory respectively (modulo two constants), together with the quantum-corrected SUSY transformations which close properly. This constitutes a complete unambiguous proof of off-shell non-renormalization theorems.

Fully off-shell effective action and its supersymmetry in matrix theory: II

In a previous study, we computed the fully off-shell effective action Γ and the corresponding quantum-corrected supersymmetry (SUSY) transformation operator δϵ for the so-called source–probe configuration in matrix theory at one loop at order four in the derivative expansion, and showed that they satisfy the SUSY Ward identity δϵΓ = 0. In this paper, starting from the most general form of Γ, we demonstrate that, conversely, given such δϵ the SUSY Ward identity determines Γ uniquely to the order specified above. Our demonstration does not require explicit knowledge of the quantum-corrected supersymmetry transformation and hence strongly suggests that the uniqueness property would persist to all orders in perturbation theory.

A theorem on the power of supersymmetry in Matrix theory

For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): let δ be a quantum-corrected effective SUSY transformation operator expandable in powers of the coupling constant g as δ=∑ n⩾0 g 2 n δ ( n) , where δ (0) is of the tree-level form. Then, apart from an overall constant, the SUSY Ward identity δΓ=0 determines the off-shell effective action Γ uniquely to arbitrary order of perturbation theory, provided that the SO(9) symmetry is preserved. Our proof depends only on the properties of the tree-level SUSY transformation laws and does not require the detailed knowledge of quantum corrections.

Fully off-shell effective action and its supersymmetry in matrixtheory

As a step toward clarification of the power of supersymmetry(SUSY)in matrix theory, a complete calculation, including all the spin effects, isperformed of the effective action of a probe D-particle, moving along anarbitrary trajectory in interaction with a large number of coincidentsource D-particles, at one-loop at order four in the derivative expansion.Furthermore, exploiting the SUSY Ward identity developed previously, thequantum-corrected effective supersymmetry transformation laws areobtained explicitly to the relevant order and are used to verify theSUSY-invariance of the effective action. Assuming that the agreementwith 11-dimensional supergravity persists, our result can be regarded asa prediction for the supergravity calculation, which, as yet unavailable, is knownto be highly non-trivial.

Effective potential for theory in three-dimensional curved spacetime

We calculate the effective potential for a gauged scalar field theory with minimal coupling to gravity, in (2 + 1)-dimensional curved spacetime using mean-field-theory approximation techniques. Gauge independence of the off-shell effective action is ensured by working within the framework of the Vilkovisky-DeWitt approach.

CENTRAL CHARGE AS THE ORIGIN OF HOLOMORPHIC EFFECTIVE ACTION IN N = 2 GAUGE THEORY

We show explicitly that the perturbative holomorphic contribution to the off-shell effective action of N=2 U(1) gauge supermultiplet is an entire effect of the minimal coupling to a hypermultiplet with the mass generated by a central charge in N = 2 superalgebra. The central charge is induced by a constant vacuum N = 2 gauge superfield strength spontaneously breaking the automorphism U (1)R symmetry of N = 2 superalgebra. We use the manifestly off-shell supersymmetric harmonic superspace techniques of quantum calculations with the central charge-massive hypermultiplet propagator.

Effective action of the N = 2 Maxwell multiplet in harmonic superspace

We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.

Modified BFV quantization of membranes and BRST invariant boundary conditions on the ghost fields

The covariant BRST off-shell effective action for the open and closed membranes is obtained. Our result generalizes Fujikawa's on-shell effective action for membranes. We found boundary conditions on the ghost fields, which are necessary in order to obtain the off-shell nilpotency of the BRST charge for the open membrane. We also proved that these boundary conditions on the ghost fields are invariant under BRST transformations and are the generalization to the Kato - Ogawa boundary conditions for the open bosonic string.

DYNAMICS OF MAGNETIC FIELDS IN MAXWELL, YANG–MILLS AND CHERN–SIMONS THEORIES ON THE TORUS

We reconsider the problem of uniform magnetic fields passing perpendicularly through a two-torus. We focus on dynamical effects from nonintegrable phases on the torus at nonzero B and from magnetic fields themselves in the vacuum. The spectrum is computed and is shown to be always independent of the nonintegrable phases on the torus. It is concluded that a Chern–Simons term will always be induced by radiative corrections to fermions on the torus when B ≠ 0. The special case of an electromagnetically uncharged anyon gas is noted and shown to be a system whose spectrum can depend on the nonintegrable phases in the two torus directions, subject to a consistency requirement. In three and four dimensions dynamical symmetry breaking of non-Abelian fields and associated condensate formation is possible by radiative corrections. The classification of non-Abelian magnetic fields in terms of "flux integers" is discussed, and a method for obtaining such integers for an arbitrary gauge algebra is presented which provides a rigorous generalization of 't Hooft's su(2) classification. Finally, we remark on the off-shell effective action in Chern–Simons theory.

One-loop Vilkovisky-DeWitt counterterms for two-dimensional gravity plus scalar field theory.

The divergent part of the one-loop off-shell effective action is computed for a single scalar field coupled to the Ricci curvature of 2D gravity ($c \phi R$), and self interacting by an arbitrary potential term $V(\phi)$. The Vilkovisky-DeWitt effective action is used to compute gauge-fixing independent results. In our background field/covariant gauge we find that the Liouville theory is finite on shell. Off-shell, we find a large class of renormalizable potentials which include the Liouville potential. We also find that for backgrounds satisfying $R=0$, the Liouville theory is finite off shell, as well.

Remarks on gauge dependence of off-shell effective action

For a wide class of gauge conditions we demonstrate that the gauge dependence of off-shell effective action is due to the nonzero vacuum expectation value of quantum fluctuations. We construct a new perturbative expansion which gives gauge-independent effective action at least at one loop.

A Kallosh theorem for BF-type topological field theory

A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the “no Vilkovisky-DeWitt” gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed.

The Vilkovisky-De Witt effective action in BF-type topological field theories

The one-loop off-shell effective action is reexamined for the case of BF theories in three dimensions. Within the context of the Vilkovisky-DeWitt reparametrization invariant framework, it is shown how the choice of an acceptable field space metric is crucial for obtaining gauge invariant results, even when this metric is field independent. It is found that the phase contribution to the one-loop effective action is proportional to the pure Chern-Simons term. The possible dependence of these results on the choice of field metric is briefly discussed.

The effective action in (2 + 1)-dimensional gravity and generalized BF topological field theory

The one-loop off-shell effective action is studied for the case of generalized BF theories in three dimensions, including, for example, (2 + 1)-dimensional gravity with a cosmological constant. The phase contribution to the effective action, originating from the η-function of a particular first order operator, is calculated using a momentum space technique. It is found that the η-function is proportional to the classical action.