Collective String Field Theory of Matrix Models in the BMN Limit
A. Jevicki
João Rodrigues2004, International Journal of Modern Physics A
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
We develop a systematic procedure for deriving canonical string field theory from large N matrix models in the Berenstein-Maldacena-Nastase limit. The approach, based on collective field theory, provides a generalization of standard string field theory.
Figures (3)
Related papers
Derivation of string field theory from the large N Berenstein-Maldacena-Nastase limit
Physical Review D, 2003
Derivation of String Field Theory from the Large N BMN Limit
Eprint Arxiv Hep Th 0305042, 2003
We continue the development of a systematic procedure for deriving closed string pp wave string field theory from the large N Berenstein-Maldacena-Nastase limit. In the present paper the effects of the Yang-Mills interaction are considered in detail for general BMN states. The SFT interaction with the appropriate operator insertion at the interaction point is demonstrated.
String field theory for d⩽0 matrix models via Marinari-Parisi
Physics Letters B, 1992
We generalize the Marinari-Parisi definition for pure two dimensional quantum gravity (k = 2) to all non unitary minimal multicritical points (k ≥ 3). The resulting interacting Fermi gas theory is treated in the collective field framework. Making use of the fact that the matrices evolve in Langevin time, the Jacobian from matrix coordinates to collective modes is similar to the corresponding Jacobian in d = 1 matrix models. The collective field theory is analyzed in the planar limit. The saddle point eigenvalue distribution is the one that defines the original multicritical point and therefore exhibits the appropriate scaling behaviour. Some comments on the nonperturbative properties of the collective field theory as well as comments on the Virasoro constraints associated with the loop equations are made at the end of this letter. There we also make some remarks on the fermionic formulation of the model and its integrability, as a nonlocal version of the non linear Schrödinger model.
Matrix string theory
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.
Continuum Limits of Berenstein-Maldacena-Nastase Matrix Theory: Where is the (Non-Abelian) Gauge Group?
Physics Letters B, 2003
Collective field theory of a singular supersymmetric matrix model
Physical Review D, 1995
The supersymmetric collective field theory with the potential v ′ (x) = ωx − η x is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The x space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
Discrete-state moduli of string theory from the c = 1 matrix model
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.
Partition Functions of Matrix Models: First Special Functions of String Theory
International Journal of Modern Physics A, 2004
Even though matrix model partition functions do not exhaust the entire set of τ -functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial nature of quantum gravity and string theory. We propose to consider matrix model partition functions as new special functions. This means they should be investigated and put into some standard form, with no reference to particular applications. At the same time, the tables and lists of properties should be full enough to avoid discoveries of unexpected peculiarities in new applications. This is a big job, and the present paper is just a step in this direction. Here we restrict our consideration to the finite-size Hermitean 1-matrix model and concentrate mostly on its phase/branch structure arising when the partition function is considered as a D-module. We discuss the role of the CIV-DV prepotential (as generating a possible basis in the linear space of solutions to the Virasoro constraints, but with a lack of understanding of why and how this basis is distinguished) and evaluate first few multiloop correlators, which generalize semicircular distribution to the case of multitrace and non-planar correlators. § • One of the goals of generic string theory [1] is to identify the properties of partition functions of various string models. These are defined as generating functions of all the correlators in a given quantum theory. Associated with the three existing formulations of quantum mechanics (linear algebra of operators in the Hilbert and Fock spaces, wave equations, path integral), there are three possible descriptions/definitions of the partition function: as a matrix element, as a solution to a system of linear differential equations (as an element of a D-module), as a (functional) integral over trajectories in configuration and/or phase space (over field configurations). These very different definitions emphasize different properties of partition functions, and their equivalence implies deep and non-trivial relations and symmetries. Among these implications, there are integrability properties of partition functions, placing them into the class of generalized τ -functions [2], which satisfy infinite sets of compatible nonlinear difference-differential equations, (generalized Hirota equations). Moreover, partition functions of different models are often related by dualities and/or mirror-like symmetries. Despite their general definitions and symmetries, partition functions are rarely expressible through conventional special functions and possess complicated analytical properties, with all kinds of singularities and branchings.
Collective field theory of the matrix-vector models
Nuclear Physics B, 1996
We construct collective field theories associated with one-matrix plus r vector models. Such field theories describe the continuum limit of spin Calogero Moser models. The invariant collective fields consist of a scalar density coupled to a set of fields in the adjoint representation of U(r). Hermiticity conditions for the general quadratic Hamiltonians lead to a new type of extended non-linear algebra of differential operators acting on the Jacobian. It includes both Virasoro and SU(r) (included in sl(r, C) × sl(r, C)) current algebras. A systematic construction of exact eigenstates for the coupled field theory is given and exemplified.
String interactions from Matrix string theory
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.
Related topics
Related papers
Continuum Limit (S) of BMN Matrix Model: Where is the (Nonabelian) Gauge Group?
Arxiv preprint hep-th/0206239, 2002
The One Dimensional Matrix Model and String Theory
Arxiv preprint hep-th/9211085, 1992
We discuss the basic features of the double scaling limit of the one dimensional matrix model and its interpretation as a two dimensional string theory. Using the collective field theory formulation of the model we show how the fluctuations of the collective field can be interpreted as the massless "tachyon" of the two dimensional string in a linear dilaton background. We outline the basic physical properties of the theory and discuss the nature of the Smatrix. Finally we show that the theory admits of another interpretation in which a certain integral transform of the collective field behaves as the massless "tachyon" in the two dimensional string with a blackhole background. We show that both the classical background and the fluctuations are non-singular at the black hole singularity.
String Theory and Matrix Models
String Theory in a Nutshell, 2011
It is generally accepted that the double-scaled 1D matrix model is equivalent to the c = 1 string theory with tachyon condensation. There remain however puzzles that are to be claried in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. W e discuss some of the issues that are related to the space-time interpretation of matrix models, in particular, the questions of leg poles, causality, and black hole background. Finally, a speculation about a possible connection of a deformed matrix model with the idea of Dirichret brane is presented.
Stochastic Hamiltonians for noncritical string field theories from double-scaled matrix models
Physical Review D, 1996
We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest c = 0 case, we derive the explicit forms of the Hamiltonians for the higher critical case k = 3 (which corresponds to c = −22/5) and for the case c = 1/2, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and W 3 algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.
BPS condensates, matrix models and emergent string theory
Journal of High Energy Physics, 2007
A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large N using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the S 5. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of "string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a quantum description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum limit), but also its quantum canonical structure. Therefore, it provides an alternative method of testing the AdS/CFT correspondence without the need of integrability.
Two-matrix model and c = 1 string theory
Physics Letters B, 1995
We show that the most general two-matrix model with bilinear coupling underlies c = 1 string theory. More precisely we prove that W 1+∞ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such twomatrix model, correspond exactly to the W 1+∞ constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the c = 1 string theory.
A matrix model for heterotic and type I string theory
Nuclear Physics B, 1999
We consider Heterotic string theories in the DLCQ. We derive that the matrix model of the Spin(32)/Z 2 Heterotic theory is the theory living on N D-strings in type I wound on a circle with no Spin(32)/Z 2 Wilson line on the circle. This is an O(N) gauge theory. We rederive the matrix model for the E 8 × E 8 Heterotic string theory, explicitly taking care of the Wilson line around the lightlike circle. The result is the same theory as for Spin(32)/Z 2 except that now there is a Wilson line on the circle. We also see that the integer N labeling the sector of the O(N) matrix model is not just the momentum around the lightlike circle, but a shifted momentum depending on the Wilson line. We discuss the aspect of level matching, GSO projections and why, from the point of view of matrix theory the E 8 ×E 8 theory, and not the Spin(32)/Z 2 , develops an 11'th dimension for strong coupling. Furthermore a matrix theory for type I is derived. This is again the O(N) theory living on the D-strings of type I. For small type I coupling the system is 0+1 dimensional quantum mechanics.
6 STRING THEORY AND MATRIX MODELS a
2016
It is generally accepted that the double-scaled 1D matrix model is equivalent to the c = 1 string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. We discuss some of the issues that are related to the space-time interpretation of matrix models, in particular, the questions of leg poles, causality, and black hole background. Finally, a speculation about a possible connection of a deformed matrix model with the idea of Dirichret brane is presented.
2D string theory as normal matrix model
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.
A new continuum limit of matrix models
Physics Letters B, 2008
We define a new scaling limit of matrix models which can be related to the method of causal dynamical triangulations (CDT) used when investigating twodimensional quantum gravity. Surprisingly, the new scaling limit of the matrix models is also a matrix model, thus explaining why the recently developed CDT continuum string field theory (arXiv:0802.0719) has a matrix-model representation (arXiv:0804.0252).
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.