Gauge hierarchy in a supersymmetric model

In a globally supersymmetric gauge theory with two distinct mass scales, the possible limitation on the gauge hierarchy due to the structure of the loop-corrected Higgs potential is shown to be absent. Also it has been demonstrated that the supersymmetry forces the large corrections to the two-point Greens functions of the light fields from the quadratic divergences and the logarithmic divergences with large coefficients to be zeroseparately. This would, therefore, allow a gauge hierarchy as large as desired.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Gauge-invariant reformulation of an anomalous gauge theory

An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the "gauge" A0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2+ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2+ and 2− particles of equal mass, as well as a massive pseudoscalar.

Euclideanization, topological theories, higher dimensions and all that

It is shown that the euclideanized Yukawa theory, with the Dirac fermion belonging to an irreducible representation of the Lorentz group, is not bounded from below. A one parameter family of supersymmetric actions is presented which continuously interpolates between the N = 2 SSYM and the N = 2 supersymmetric topological theory. In order to obtain a theory which is bounded from below and satisfies Osterwalder-Schrader positivity, the Dirac fermion should belong to a reducible representation of the Lorentz group and the scalar fields have to be reinterpreted as the extra components of a higher dimensional vector field.

Quantum corrections to screening at strong coupling

We compute a certain class of corrections to (specific) screening lengths in strongly coupled non-abelian plasmas using the AdS/CFT correspondence. In this holographic framework, these corrections arise from various higher curvature interactions modifying the leading Einstein gravity action. The changes in the screening lengths are perturbative in inverse powers of the `t Hooft coupling or of the number of colors, as can be made precise in the context where the dual gauge theory is superconformal. We also compare the results of these holographic calculations to lattice results for the analogous screening lengths in QCD. In particular, we apply these results within the program of making quantitative comparisons between the strongly coupled quark-gluon plasma and holographic descriptions of conformal field theory. (c) 2012 Elsevier B.V. All rights reserved.

Black hole formation at the correspondence point

We study the process of bound state formation in a D-brane collision. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is pair creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a large black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and time scale for formation of a bound state agree at the correspondence point. The time scale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity.

A matrix model for QCD: QCD color is mixed

We use general arguments to show that colored QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colorless state can never evolve into two colored states by unitary evolution. Furthermore, the mean energy in such a mixed colored state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas(3) and Singer.(2) This model, a (0 + 1)-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large N QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for N = 2 and 3 (colors). Incidentally the considerations here are generic and apply to any non-Abelian gauge theory.

Quantum fluctuations and thermal dissipation in higher derivative gravity

In this paper, based on the AdS(2)/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z -> infinity). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z = 5 fixed point. (C) 2015 The Author. Published by Elsevier B.V.

3D gravity, Chern-Simons and higher spins: A mini introduction

We give a review on (a) elements of (2 + 1)-dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.