Algebraic simplifications in supergravity theories

Supercovariant derivatives and supercovariant field strengths are used to put the fermionic equations of motion derived from supergravity theories in an elegant form. These results apply also to the SO(4) extended supergravity theory which is presented here. We discuss how to obtain more compact proofs of the invariance of the supergravity actions already known. In particular for the SO(2) theory a set of new auxilary fields is introduced which linearizes the equation of motion of the $\text{spin}\text{-}\text{3}\text{2}$ field.     

Perturbative and global anomalies in supergravity theories

Perturbative and global anomalies in supergravity theories are reviewed. The existence of a matter and gauge coupled supergravity theory in six dimensions withE ₆×E ₇×U(1) symmetry and highly nontrivial anomaly cancellations is emphasised. The possible string origin of this theory is posed as an open problem, study of which may lead to discovery of new ways to construct/compactify heterotic superstrings.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.I would like to thank J. Strathdee for a stimulating discussion on the possible string origins of theE ₆×E ₇×U(1) theory, and E. Bergshoeff for his critical reading of this paper.     

Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

We investigate a 6 D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant.Each stress-energy tensor T_(ab)~i on the brane is shown to be similar to a constant vacuum energy.This is consistent with the Randall-Sundrum model,in which each 3-brane Lagrangian yielded a constant vacuum energy.By adopting an anisotropic metric ansatz,we obtain the 5 D Friedmann-Robertson-Walker field equations.In a slightly later period,the expansion of the universe is proportional to the square root of time,t~(1/2),which is similar to the period of the radiation-dominated regime.Moreover,we investigate the case with two a(t) and two b(t).In a large range of t,we obtain the 3 D effective cosmological constant Λ_(eff)=-2Ω/30,which is independent of the integral constant.Here,the scale factor is an exponential expansion,which is consistent with our present observation of the universe.Our results demonstrate that it is possible to construct a model that solves the dark energy problem,while guaranteeing a positive brane tension.     

Torsion and curvature in higher dimensional supergravity theories

This work is an extension of Dragon's theorems to higher dimensional space-time. We show that the first set of Bianchi identities allows us to express the curvature components in terms of torsion components and its covariant derivatives. It is also shown that the second set of Bianchi identities does not give any new information which is not already contained in the first one.     

Anomaly-free supergravity and super-Yang-Mills theories in ten dimensions

We formulate in ten dimensions a supergravity theory coupled to a super-Yang-Mills theory through the Green-Schwarz ansatz, which ensures chiral anomaly cancellation. The formulation is obtained by fixing suitable constraints in the superspace and solving the Bianchi identities. In this way we obtain the whole set of equations of motion. They are characterized by highly non-polynomial expressions, when expressed only in terms of the physical superfields. We discuss the problem of the massive modes appearing in some of these equations.     

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

We demonstrate a few striking similarities and some glaring differences between (i) the free four- (3+1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two- (1+1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. With the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge-invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.     

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N=2U(k) SYM on R²×(Fuzzy R²) around the minimum of k-coincident fuzzy spheres.     

Neutrino radiative decay in N=1 supergravity theories

We show that the supersymmetrization of models where neutrinos acquire mass through the see-saw mechanism allows for tau neutrinos heavier than 15–20 MeV to decay radiatively in a cosmologically safe way (i.e. with a lifetime τ_v⩽5×10³s).     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Holomorphic Chern-Simons-Witten theory: From 2D to 4D conformal field theories

It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebras, the local action of which on fields of holomorphic analogues of Chern-Simons theories becomes non-local after pushing down to the action on fields of integrable 4D conformal field theories. Quantization of integrable 4D conformal field theories and relations to string theories are briefly discussed.     

Hamiltonian formulation of d = 10 supergravity theories

A method is given for deriving the hamiltonian form of the d = 10 supergravity models. It is explicitly applied to the N = 1 theory.     

Quantum interference effects in Einstein-Maxwell,supergravity and non-abelian Kaluza-Klein theories

Quantum interference effects in Einstein-Maxwell, supergravity and non-abelian Kaluza-Klein theories have been calculated following the idea of Parthasarathy, Rajasekharan and Vasedevan.     

The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms

A mechanism is exhibited which ensures that N=1, D=4 new minimal supergravity is free of Lorentz×U(1) anomalies, for any coupling to matter, although it contains an abelian chiral gauge field. This is achieved through the determination of a new supergravity algebra characterized by the presence of a U(1)×Lorentz Chern-Simon form in the field strength of a two-form gauge field. Our analysis provides therefore an example in which Chern-Simon type interactions do occur, while preserving local supersymmetry.     

Supersymmetry breaking with vanishing F-terms in supergravity theories

In conventional supergravity theories, supersymmetry is broken by a non-zero F-term, and the cosmological constant is fine tuned to zero by a constant in the superpotential W. We discuss a class of supergravity theories with vanishing F-terms but W ≠ 0 being generated dynamically. The cosmological constant is assumed to be cancelled by a non-zero D-term. In this scenario the gravity-mediated soft masses depend only on a single parameter, the gravitino mass. They are automatically universal, independently of the Kähler metric, and real. Thus, dangerous flavor or CP violating interactions are suppressed. Unlike in conventional supergravity models, the Polonyi problem does not arise.     

Supersymmetric gauge theories coupled to non-minimal and new minimal supergravity

The coupling of the various supergravity multiplets to gauge invariant theories is constructed using a chiral basis for curved superspace. It is shown thatR invariance is not required for such a construction.