Matrix models and N=2 gauge theory

We describe how the ingredients and results of the Seiberg-Witten solution to N=2 supersymmetric U(N) gauge theory may be obtained from a matrix model.Comment: 6 pages, AMSLaTeX (ws-procs9x6.cls included). Presented at QTS3 (Cincinnati, Ohio, Sept. 10-14, 2003

Two-dimensional Yang-Mills Theories Are String Theories

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be associated with maps from a string worldsheet onto M. These maps are unbranched and branched covers of M with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in M. These string theories differ from SU(N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.Comment: (two references added; one old, one recent) 14pages, Latex, BRX-TH-346, JHU-TIPAC-93001

Electroweak strings and fermions

Z-strings in the Weinberg-Salam model including fermions are unstable for all values of the parameters. The cause of this instability is the fermion vacuum energy in the Z-string background. Z-strings with non-zero fermion densities, however, may still be stable

Wilson line approach to gravity in the high energy limit

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories.Comment: 33 pages, 5 figure

Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory

The free energy in the weak-coupling phase of two-dimensional Yang-Mills theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using the techniques of Gross and Matytsin. Many features of Yang-Mills theory are universal among different gauge groups in the large N limit, but significant differences arise in subleading order in 1/N.Comment: 10 pages; no figures; LaTe

Analytical Representation of a Black Hole Puncture Solution

The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture simulations, the evolution of a single black hole leads to a well-known time-independent, maximal slicing of Schwarzschild. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example for testing and calibrating numerical codes that employ moving puncture techniques. In this Brief Report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes

Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation

We use matrix model technology to study the N=2 U(N) gauge theory with N_f massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods a_i and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve from the large-M solution of the matrix model. We show that the two cases N_f<N and N \le N_f < 2N can be treated simultaneously

The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N=2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a_i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-Witten differential or curve. We also compute the N=2 prepotential F(a) perturbatively up to the first-instanton level finding agreement with the known result

Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass

A Fermion in 2+1 dimensions, with a mass function which depends on one spatial coordinate and passes through a zero ( a domain wall mass), is considered. In this model, originally proposed by Callan and Harvey, the gauge variation of the effective gauge action mainly consists of two terms. One comes from the induced Chern-Simons term and the other from the chiral fermions, bound to the 1+1 dimensional wall, and they are expected to cancel each other. Though there exist arguments in favour of this, based on the possible forms of the effective action valid far from the wall and some facts about theories of chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this paper we present an explicit calculation of this cancellation at one loop valid even close to the wall. We show that, integrating out the ``massive'' modes of the theory does produce the Chern-Simons term, as appreciated previously. In addition we show that it generates a term that softens the high energy behaviour of the 1+1 dimensional effective chiral theory thereby resolving an ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61