Matrix string theory and its moduli space

Nuclear Physics B, 1997

Via compactification on a circle, the matrix model of M-theory proposed by Banks et al suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states. * Here we work in string units α = 1. A derivation of (1) from matrix theory and a discussion of our normalizations is given in the appendix.

Physics Letters B, 1998

Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U (N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via joining/splitting interactions similar to those of string field theory. We construct them starting from branched coverings of Riemann surfaces. For the class of them which we analyze in detail the construction can be made explicit in terms U (N) affine Toda field theories.

Nuclear Physics B, 1999

The Matrix String Theory, i.e. the two dimensional U(N) SYM with N = (8, 8) supersymmetry, has classical BPS solutions that interpolate between an initial and a final string configuration via a bordered Riemann surface. The Matrix String Theory amplitudes around such a classical BPS background, in the strong Yang-Mills coupling, are therefore candidates to be interpreted in a stringy way as the transition amplitude between given initial and final string configurations. In this paper we calculate these amplitudes and show that the leading contribution is proportional to the factor g −χ s , where χ is the Euler characteristic of the interpolating Riemann surface and g s is the string coupling. This is the factor one expects from perturbative string interaction theory.

Nuclear Physics B, 1995

We propose a new formulation of the space-time interpretation of the c = 1 matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the fermi vacuum on both sides of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of spacetime gravity. We reproduce the known results for the string theory tree level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent nonperturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

Nuclear Physics B, 2003

We show that the c = 1 bosonic string theory at finite temperature has two matrixmodel realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.

Nuclear Physics B - Proceedings Supplements, 2002

The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space-time appears dynamically. It is possible that lower dimensional universes dominate the theory, therefore providing a dynamical solution to the reduction of space-time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.

Physics Letters B, 1997

It has been proposed recently that, in the framework of M(atrix) theory, N = 8 supersymmetric U (N ) Yang-Mills theory in 1+1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM 1+1 gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2, Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.

2013

We explore the moduli space of heterotic strings in two dimensions. In doing so, we introduce new lines of compactified theories with Spin(24) gauge symmetry and discuss compactifications with Wilson lines. The phase structure of d = 2 heterotic string theory is examined by classifying the hypersurfaces in moduli space which support massless quanta The past few years have seen a resurgence of interest in two-dimensional string theory. Just as in the first period of interest in d = 2 strings (for a review see [1-3]), the latest studies have used these theories as toy models of phenomena in higher dimensions. Topics of recent interest include tachyon condensation and D-brane decay [4,5], flux vacua [6,7]

Journal of High Energy Physics, 2004

We derive the four dimensional N = 1/2 super Yang-Mills theory from tree-level computations in RNS open string theory with insertions of closed string Ramond-Ramond vertices. We also study instanton configurations in this gauge theory and their ADHM moduli space, using systems of D3 and D(-1) branes in a R-R background.

2004

In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of compactification via orbifolding for deconstructed IIA strings. In the continuum limit, our matrix mechanics becomes a (2 + 1)-dimensional Yang-Mills theory with 16 supercharges. At the discrete level, we are able to construct explicitly the solitonic states that correspond to membranes wrapping on the compactified torus in target space. These states have a manifestly SL(2, Z)-invariant spectrum with correct membrane tension, and give rise to an emergent flat dimension when the compactified torus shrinks to vanishing size.