Sunil Mukhi

D2 to D2

Starting from maximally supersymmetric (2+1)d Yang-Mills theory and using a duality transformation due to de Wit, Nicolai and Samtleben, we obtain the ghost-free Lorentzian 3-algebra theory that has recently been proposed to describe M2-branes. Our derivation does not invoke any properties of 3-algebras. Being derivable from SYM, the final theory is manifestly equivalent to it on-shell and should not be thought of as the IR limit that describes M2-branes, though it does have enhanced R-symmetry as well as superconformal symmetry off-shell.

F-theory at Constant Coupling

The subspace of the moduli space of F-theory on K3 over which the coupling remains constant develops new branches at special values of this coupling. These values correspond to fixed points under the SL(2,Z) duality group of the type IIB string. The branches contain points where K3 degenerates to orbifolds of the four-torus by Z3,Z4 and Z6. A singularity analysis shows that exceptional group symmetries appear on these branches, including pure E8 × E8, although SO(32) cannot be realised in this way. The orbifold points can be mapped to a kind of non-perturbative generalization of a IIB orientifold, and to M-theory orbifolds with non-trivial action on 2-brane wrapping modes.

Brane constructions, conifolds and M-theory

We show that a set of parallel 3-brane probes near a conifold singularity can be mapped onto a configuration of intersecting branes in type IIA string theory. The field theory on the probes can be explicitly derived from this formulation. The intersecting-brane metric for our model is obtained using various dualities and related directly to the conifold metric. The M-theory limit of this model is derived and turns out to be remarkably simple. The global symmetries and counting of moduli are interpreted in the M-theory picture.

Two-dimensional black hole as a topological coset model of c = 1 string theory

We show that a special superconformal coset (with c = 3) is equivalent to c = 1 matter coupled to two-dimensional gravity. This identification allows a direct computation of the correlation functions of the c =1 non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a euclidean two-dimensional black hole, in which the ghost and matter systems are mixed.

Orbifolds of M-theory

Abstract We study Z 2 -orbifolds of 11-dimensional M-theory on tori of various dimensions. The most interesting model (besides the known S 1 / Z 2 case) corresponds to T 5 / Z 2 for which we argue that the resulting six-dimensional theory is equivalent to the type IIB string compactified on K3. Gravitational anomaly cancellation plays a crucial role in determining what states appear in the twisted sector. Most of the other models appear to break spacetime supersymmetry. We observe that M-theory tends to produce chiral compactifications on orbifolds, and that our results may provide an insight into the mechanism by which twisted-sector states arise in this hypothetical theory.

BPS nature of 3-string junctions

We study BPS-saturated classical solutions for the world-sheet theory of a D-string in the presence of a point charge. These solutions are interpreted as describing planar 3-string junctions, which arise because the original D-string is deformed by the presence of the inserted charge. We compute the angles of the junctions and show that the vector sum of string tensions is zero, confirming a conjecture of Schwarz that such configurations are BPS states.

The geometric background-field method, renormalization and the Wess-Zumino term in non-linear σ-models

A simple recursive algorithm is presented which generates the reparametrization-invariant background-field expasion for non-linear σ-models on manifolds with an arbitrary riemannian metric. The method is also applicable to Wess-Zumino terms and to counterterms. As an example, the general-metric model is expanded to sixth order and compared with previous results. For locally symmetric spaces, we actually obtain a general formula for the nth order term. The method is shown to facilitate the study of models with Wess-Zumino terms. It is demonstrated that, for chiral models, the Wess-Zumino term is unrenormalized to all orders in perturbation theory even when the model is not conformally invariant.

Multiple Membranes in M-theory

We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent diffi culties with constructing a maximally supersymmetric lagrangian with the appropriate field content and symmetries, we introduce 3-algebras and show how they allow for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then demonstrate that these theories are equivalent to conventional superconformal Chern-Simons gauge theories at level k, but with bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain sub class of models with configurations of M2-branes on Zk orbifolds. These models give rise to a whole new gauge/gravity duality in the form of an AdS4/CFT3 correspondence. We also discuss mass deformations, higher derivative corrections, and the possibility of extracting information about M5-brane physics.

On the classification of rational conformal field theories

We propose a method for classifying rational conformal field theories in terms of the differential equation satisfied by their characters.

Orbifold and orientifold compactifications of F-theory and M-theory to six and four dimensions

We study orbifold compactifications of F-theory which lead to N = 1 supersymmetry in six and four space-time dimensions. These are dual to specific orientifolds of M-theory, and in many cases to orientifolds of type IIB string theory. The equivalences are demonstrated by mapping the orbifolding transformations in the F-, M- and string theories to each other using dualities. We observe that M- and F-theory appear to possess a property similar to discrete torsion in string theory. This is related to an ambiguity recently noted by Polchinski in the orientifold projection for six-dimensional models. The four-dimensional compactifications exhibit similar features, from which we predict the existence of certain new orientifolds of type IIB. Some orbifolds with higher supersymmetry are also examined.