Matrix Description of Interacting Theories in Six Dimensions

We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of $N$ instantons in \IR^4.Comment: 10 pages, harvmac bi

A brief review of "little string theories"

This is a brief review of the current state of knowledge on "little string theories", which are non-gravitational theories having several string-like properties. We focus on the six dimensional maximally supersymmetric "little string theories" and describe their definition, some of their simple properties, the motivations for studying them, the DLCQ and holographic constructions of these theories and their behaviour at finite energy density. (Contribution to the proceedings of Strings '99 in Potsdam, Germany.)Comment: 11 pages, contribution to Strings '99 proceeding

Unitarity of noncommutative field theories from string theory

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.Comment: 8 pages, no figures. Work done in collaboration with A. Bassetto and R. Valandro (Padua Univ.). Submitted for the proceedings of the conference "Spacetime and Fundamental Interactions: Quantum Aspects. A conference to honour A.P.Balachandran's 65th birthday", Vietri, 26-31 May 200

Long Strings, Anomaly Cancellation, Phase Transitions, T-duality and Locality in the 2d Heterotic String

We study the noncritical two-dimensional heterotic string. Long fundamental strings play a crucial role in the dynamics. They cancel anomalies and lead to phase transitions when the system is compactified on a Euclidean circle. A careful analysis of the gauge symmetries of the system uncovers new subtleties leading to modifications of the worldsheet results. The compactification on a Euclidean thermal circle is particularly interesting. It leads us to an incompatibility between T-duality (and its corresponding gauge symmetry) and locality.Comment: 36 pages, 2 figure

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions

We consider general aspects of N=2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U(1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to ``mirror symmetries'' of 3d N=4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU(N_c) gauge groups with N_f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.Comment: 40 pages, harvma

Gauge Symmetry Breaking through Soft Masses in Supersymmetric Gauge Theories

Effects of soft breaking in N=1 supersymmetric gauge theories are studied. For N_f < N_c, we include the dynamics of the non-perturbative superpotential and use the original (s)quark and gauge fields. For N_f > N_c +1, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group SU(N_f-N_c). The mass squared of the squarks can be negative triggering spontaneous breakdown of flavor and color symmetry. The general condition for stability of the vacuum is derived. We determine the breaking pattern, determine the spectrum and argue that the masses vary smoothly as one crosses from the Higgs phase into the confining phase, thus exhibiting complementarity.Comment: Contribution to Inauguration Conferference of Asia Pacific Center for Theoretical Physics, 4-10 June, 1996, Seoul National University; LaTeX, no macros neede

A Note on Unitarity of Non-Relativistic Non-Commutative Theories

We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be restored (at least at the level of one-to-one scattering amplitude) by adding new states to the theory. This is a signal that the model cannot be embedded in a natural way in string theory.Comment: 6 pages, 2 figures. References adde

Tests of Seiberg-like Duality in Three Dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N=4 gauge theories realized by monopole operators.Comment: 36 pages, 5 figure

Locality, Causality and Noncommutative Geometry

We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative spacetime. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.Comment: 16 pages, LaTeX, 4 figure