Chiral Supergravity Research Articles

Induced chiral supergravities in 2D

We analyze actions for 2D supergravities induced by chiral conformal supermatter. The latter may be thought of as described at the classical level by superspace actions invariant under super-reparametrization, super-Weyl and super-Lorentz transformations. Upon quantization various anomalies appear which characterize the nontrivial induced actions for the supergravitational sector. We derive these induced actions using a chiral boson to represent the chiral inducing matter. We show that they can be defined in a super-reparametrization invariant way, but with super-Weyl and super-Lorentz anomalies. We consider the case of (1, 0) and (1, 1) supergravities by working in their respective superspace formulations and investigate their quantization in the conformal gauge. The actions we consider arise naturally in off-critical heterotic and spinning strings. In the conformal gauge, they correspond to chiral extensions of the super-Liouville theory.

Relation between linear and nonlinear N=3,4 supergravity theories.

The effective actions for $d=2$, $N=3, 4$ chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical.

Induced ( N, 0) supergravity as a constrained Osp( N | 2) WZWN model and its effective action

A chiral ( N, 0) supergravity theory in d = 2 dimensions for any N and its induced action can be obtained by constraining the currents of an Osp( N | 2) WZWN model. The underlying symmetry algebras are the nonlinear SO( N) superconformal algebras of Knizhnik and Bershadsky. The case N = 3 is worked out in detail. We show that by adding quantum corrections to the classical transformation rules, the gauge algebra on gauge fields and currents closes. Integrability conditions on Ward identities are derived. The effective action is computed at one loop. It is finite, and can be obtained from the induced action by rescaling the central charge and fields by finite Z factors.

Complete invariant lagrangians of d = 10 N = 2 b and d = 6 N = 2 chiral supergravities

The complete lagrangians for the theories mentioned in the title, are constructed. The supersymmetry and α-symmetry of the complete lagrangian of pure d = 6 N = 2 supergravity are proved and similarly they are proved for d = 10 N = 2 b chiral supergravity in first order over Fermi fields. The algebra of symmetries is considered for both theories. An exact connection of the first one with the non-chiral theories of Nishino and Sezgin is established.

Cancellation of gravitational anomalies in d=6 supergravities

The conditions for cancellation of gravitational anomalies in d=6 chiral supergravities based on the systematic use of index theorems are examined here. The authors point out the minimal necessary combinations of chiral fermions (with spin 3/2 and 1/2) and (anti-) self-dual antisymmetric tensors, as well as the corresponding combinations of N=1, d=6 supermultiplets that ensure cancellation of gravitational anomalies.

Invariant action principle for six-dimensional chiral supergravities

Complete invariant lagrangians for N = 4 b and N = 2 six-dimensional chiral supergravities which contain (anti)self-duality equations among their equations of motion are constructed, and the algebra of symmetries of these lagrangians is considered.

Maximal supergravities in SU(8/1).

It is shown that four- and ten-dimensional chiral maximal supergravities can be described in SU(8/1) superalgebra. The supermultiplets of both of these theories belong to an irreducible representation of SU(8/1). Dimensional reduction is also discussed.

Self-duality for interacting fields: Covariant field equations for six-dimensional chiral supergravities

We determine the supersymmetric coupling of chiral N = 4 b supergravity in six dimensions to an arbitrary number n of anti-self-dual tensor multiplets. In a novel phenomenon, the five self-duality and n anti-self-duality conditions for the two-index tensors are modified by the scalar interactions to be non-diagonal in terms of the elementary tensor gauge fields, which transform irreducibly under a global SO(5, n) invariance. The 5 n scalar fields parametrize the coset manifold SO(5,n) [ SO(5) × SO(n)] . The truncated N = 2 systems, in which the n scalar parameterize the space SO(n, 1) SO(n) , are derived and found to have analogous properties. In general the theories do not admit action principles possessing manifest linearly realized Lorentz invariance, so the construction is effected at the level of the supersymmetry transformations and field equations. Finally, we speculate on generalizations including N = 2 vector matter, and comment on the possible implications of our results for chiral superstring models.

O(2) string theory with a Wess-Zumino term.

N-italic = 2 chiral conformal supergravity is coupled to a (2,0) supersymmetric nonlinear sigma model with a Wess-Zumino term. This Lagrangian can describe a consistent O(2) string theory in more than 2 space-time dimensions.

GLOBAL ANOMALIES IN SIX DIMENSIONS

Applying Witten’s formula for global gauge and gravitational anomalies to 6-dimensional supergravities, we find: (a) The perturbatively anomaly free N=4 chiral supergravity coupled to 21 tensor multiplets is global anomaly free for any choice of space-time manifold with vanishing third Betti number (b3); (b) The perturbatively anomaly free matter coupled N=2 chiral super-gravities with arbitrary number of tensor multiplets, whose Yang-Mills gauge groups do not include G2, SU(2), or SU(3) are free of global anomalies if the theory is formulated on S6. In the case of 9 tensor multiplets coupled to supergravity, this result holds for any space-time with vanishing b3. (c) The N=6 chiral supergravity has perturbative gravitational anomalies and therefore the global anomalies need not be considered in this case.

Anomaly Freedom in Chiral Supergravities

We give criteria for anomaly cancellations in chiral Yang-Mills supergravities (including dual formulations of the theories) in 6, 8 and 10 dimensions.

Local supersymmetry anomaly in two dimensions

We study the local supersymmetry anomaly by constructing an N = 1 (counted by Majorana-Weyl spinors) chiral supergravity model in two dimensions. There is the local supersymmetry anomaly as well as the gravitational anomaly. We obtain the linearized forms of these anomalies by perturbation calculation. The full non-linear forms are obtained by finding a solution to the Wess-Zumino consistency condition. These anomalies can be derived from the supersymmetric extension of the Chern-Simons invariant in three dimensions.

Anti-de sitter × S 1 × M 5compact solutions for N = 2, d = 10 chiral supergravity

We construct solutions of N = 2, d = 10 chiral supergravity of the form Anti-de Sitter × S 1 × M 5, where M 5 is a compact Einstein 5-space of at least 3 possible explicit forms. We prove that two of the solutions are very likely stable against small perturbations, and give their mass spectra.

A new anomaly free chiral supergravity theory from compactification on K 3

We establish the existence at the linearized level of a new chiral N=4 extended supergravity theory in six-dimensional spacetime that could couple to the chiral N=4 antisymmetric tensor multiplet. The unique anomaly free combination occurs for 21 of the latter and the spectrum then coincides with the zero-mass sector of the N=2 ten-dimensional chiral supergravity theory compactified on K 3.