E. Sezgin

Supermembranes and Eleven-Dimensional Supergravity

Abstract We construct an action for a supermembrane propagating in d = 1 supergravity background. Using the constraints of d = 11 curved superspace, we show that the action is invariant under Siegel-type tranformations recently generalized by Hughes, Li and Polchinski. The transformation parameter is a world-volume scalar and d = 11 spacetime spinor. We also discuss the general problem of the coupling of n -dimensional extended objects to d -dimensional supergravity.

Properties of the Eleven-Dimensional Supermembrane Theory

We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N=8 world volume (rigid) supersymmetry in a “physicalâ€� gauge; we also present the field equations and transformation rules in a “lightconeâ€� gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowki)4 A— (flat 7-torus), and review some mathematical results that are relevant for path integral quantization.

Chiral compactification on Minkowski × S2 of N = 2 Einstein-Maxwell supergravity in six dimensions

Abstract We show that the U(1) gauged Einstein-Maxwell supergravity in six dimensions, spontaneously compactifies on Minkowski × S 2 , with a monopole-valued Maxwell field on S 2 . The bosomic symmetry of the background is SU(2) × U(1). The field equations fix the monopole charge to be ±1. The consequence of this is that the N = 2 supersymmetry breaks down to N = 1, and chiral fermions emerge.

Matter and Gauge Couplings of N=2 Supergravity in Six-Dimensions

Abstract We construct the couplings of a single anti-symmetric tensor multiplet, the non-compact HP (n − 1, 1) ≡ Sp (n, 1) Sp (n) × Sp (1) σ-model and a Yang-Mills multiplet with the local gauge group Sp( n ) × Sp(1) to N = 2 supergravity in d = 6. The theory has a positive definite potential. If only the Sp( n ) group is gauged, we can use the global Sp(1) invariance to realize a super-Higgs effect a la Scherk and Schwarz.

The complete N = 2, d = 6 supergravity with matter and yang-mills couplings

Abstract We derive all the quartic fermion terms in the action, and all the cubic fermion tterms in the transformation rules of the N = 2, d = 6 supergravity plus matter-coupled Yang-Mills system constructed by the authors in an earlier paper. We also show how compactification to the 4-dimensional Minkowski spacetime is always automatically realized even with fermionic condensates, based on the argument of scale covariance by Witten.

Superconformal tensor calculus and matter couplings in six dimensions

Abstract Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40+40 version of the Weyl multiplet. We also obtain a 48+48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet.

An Anomaly Free Model in Six-Dimensions

Abstract We show that a gauged supergravity theory based on E 6 × E 7 × U(1) is free of gauge and gravitational anomalies in six dimensions. It compactifies to (Minkowski) 4 × S 2 by the standard monopole mechanism. With a monopole of strength n in E 6 , the resulting four-dimensional theory exhibits chiral SO(10) × U(1) with 2| n | families (and no antifamilies). Supersymmetry is broken.

Semiclassical Quantization of the Supermembrane

Abstract We approach the quantization of the eleven-dimensional supermembrane from a semiclassical viewpoint. We quantize the fluctuations around a topologically-stabilized toroidal background, and find that the bosonic and fermionic contributions to the vacuum energy cancel. This result appears to depend crucially on the fermionic gauge symmetry and spacetime supersymmetry.

The Born-Infeld action from conformal invariance of the open superstring

Abstract We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.

Coupling of Yang-Mills to N = 4, d = 4 supergravity

Abstract We couple N = 4, d = 4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset (SO( n ,6)/[SO( n )×SO(6)])×(SU(1,1)/U(1)). Keeping the composite local SO( n )×SO(6)×U(1) invariance intact, we gauge an ( n + 6) parameter subgroup of SO( n ,6) which is either (i) SU(2)×SU(2)×H (dim H = n ), (ii) SO(4,1)×H (dim H = n −4) or (iii) SO(6,1)×H (dim H = n −15). In all these cases the theory has an indefinite potential.