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David J. Gross

Publications and source records attributed to David J. Gross.

At least 37 records · Page 2Linked to original sources
arXiv2000

Dynamics of Strings in Noncommutative Gauge Theory

We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point--- corresponding to fundamental strings stretched between the D1string and the D3 brane. We discuss the fluctuations about theN-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution.

hep-th↗
arXiv2000

Monopoles and Strings in Noncommutative Gauge Theory

We study some non-perturbative aspects of noncommutative gauge theories. We find analytic solutions of the equations of motion, for noncommutative U(1) gauge theory, that describe magnetic monopoles with a finite tension string attached. These solutions are non-singular, finite and sourceless. We identify the string with the projection of a D-string ending on a D3-brane in the presence of a constant B-field.

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arXiv2000

Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function

A systematic approach to the study of semiclassical fluctuations of strings in AdS_5 x S^5 based on the Green-Schwarz formalism is developed. We show that the string partition function is well defined and finite. Issues related to different gauge choices are clarified. We consider explicitly several cases of classical string solutions with the world surface ending on a line, on a circle or on two lines on the boundary of AdS. The first example is a BPS object and the partition function is one. In the third example the determinants we derive should give the first corrections to the Wilson loop expectation value in the strong coupling expansion of the n=4 SYM theory at large N.

hep-th↗
arXiv2000

Sphalerons, Merons and Unstable Branes in AdS

We construct unstable classical solutions of Yang-Mills theories and their dual unstable states of type IIB on AdS_5. An example is the unstable D0-brane of type IIB located at the center of AdS. This has a field theory dual which is a sphaleron in gauge theories on S^3 x R. We argue that the two are dual because both are sphalerons associated to the topology of the instanton/D-instanton. This agreement provides a non-supersymmetric test of the AdS/CFT duality. As an illustration, many aspects of Sen's hypothesis regarding the unstable branes can be seen easily in the weakly coupled dual field theory description. In Euclidean AdS the D0-branes are dual to gauge theory merons. This implies that the two ends of a D0-brane world-line carry half the charge of a D-instanton. Other examples involve unstable strings in the Coulomb phase.

hep-th↗
arXiv1999

Wilson Loops and Minimal Surfaces

The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultra-violet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5 gives a solution of the equation. We also discuss the zig-zag symmetry of the loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.

hep-th↗
arXiv1998

Twenty Five Years of Asymptotic Freedom

On the occasion of the 25th anniversary of Asymptotic Freedom, celebrated at the QCD Euroconference 98 on Quantum Chromodynamics, Montpellier, July 1998, I described the discovery of Asymptotic Freedom and the emergence of QCD.

hep-th↗
arXiv1998

Aspects of Large N Gauge Theory Dynamics as Seen by String Theory

In this paper we explore some of the features of large N supersymmetric and nonsupersymmetric gauge theories using Maldacena's duality conjectures. We shall show that the resulting strong coupling behavior of the gauge theories is consistent with our qualitative expectations of these theories. Some of these consistency checks are highly nontrivial and give additional evidence for the validity of the proposed dualities.

hep-th↗
arXiv1997

The Spectrum of a Large N Gauge Theory Near Transition from Confinement to Screening

We study the spectrum of 1+1 dimensional large $N$ QCD coupled to an adjoint Majorana fermion of mass $m$. As $m\to 0$ this model makes a transition from confinement to screening. We argue that in this limit the spectrum becomes continuous for mass greater than twice the mass of the lightest bound state. This critical mass is nothing but the threshold for a decay into two lightest states. We present numerical results based on DLCQ that appear to support our claim.

hep-th↗
arXiv1994

Oscar Klein and Gauge Theory

In this talk, delivered at the Oscar Klein Centenary Symposium in Stockholm, I review the 1938 conference held in Warsaw devoted to \lq \lq New Theories in Physics". I review all of the talks presented at this meeting and discuss in detail Klein's paper where he proposed a unified model of electromagnetism and the nuclear force that foreshadowed the later developments of non-Abelian gauge theories.

hep-th↗
arXiv1994

Mastering the Master Field

The basic concepts of non-commutative probability theory are reviewed and applied to the large $N$ limit of matrix models. We argue that this is the appropriate framework for constructing the master field in terms of which large $N$ theories can be written. We explicitly construct the master field in a number of cases including QCD$_2$. There we both give an explicit construction of the master gauge field and construct master loop operators as well. Most important we extend these techniques to deal with the general matrix model, in which the matrices do not have independent distributions and are coupled. We can thus construct the master field for any matrix model, in a well defined Hilbert space, generated by a collection of creation and annihilation operators---one for each matrix variable---satisfying the Cuntz algebra. We also discuss the equations of motion obeyed by the master field.

hep-th↗
arXiv1994

Some Properties of Large $N$ Two Dimensional Yang--Mills Theory

Large $N$ two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD$_2$ is established. Using this relation, it is shown that the Douglas--Kazakov phase transition on a cylinder is associated with the presence of a gap in the eigenvalue distributions for Wilson loops. An exact formula for the phase transition on disc with an arbitrary boundary holonomy is found. The role of instantons in inducing such transitions is discussed. The zero-area limit of the partition function on a vertex manifold is studied. It is found that this partition function vanishes unless the boundary conditions satisfy a certain selection rule which is an analogue of momentum conservation in field theory.

hep-th↗
arXiv1994

Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD

The $1/N$ expansion of the weak coupling phase of two-dimensional QCD on a sphere is constructed. It is demonstrated that the phase transition from the weak to the strong coupling phase is induced by instantons. A double scaling limit of the theory at the point of the phase transition is constructed, the value of string susceptibility is determined to be $γ_{str}=-1$. The possibility of instanton induced large $N$ phase transitions in four dimensional QCD is explored.

hep-th↗
arXiv1993

Two Dimensional QCD is a String Theory

The partition function of two dimensional QCD on a Riemann surface of area $A$ is expanded as a power series in $1/N$ and $A$. It is shown that the coefficients of this expansion are precisely determined by a sum over maps from a two dimensional surface onto the two dimensional target space. Thus two dimensional QCD has a simple interpretation as a closed string theory.

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arXiv1992

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.

hep-th↗
arXiv1992

Two Dimensional QCD as a String Theory

I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean manifold. If this is related to a two-dimensional string theory then many of the coefficients of the ${1\over N}$ expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.

hep-th↗
arXiv1992

Asymptotic Freedom and the Emergence of QCD

I describe our understanding of the strong interactions at the end of the 1960's and the impact of the experiments on deep inelastic scattering. I recall the steps that lead from the attempts to understand these experiments to the discovery of asymptotic freedom in 1973 and the subsequent rapid emergence, development and acceptance of the non-Abelian gauge theory of color (QCD) as the theory of the strong interactions.

hep-ph↗
arXiv1992

Some Remarks About Induced QCD

Migdal and Kazakov have suggested that lattice QCD with an adjoint representation scalar in the infinite coupling limit could induce QCD. I find an exact saddlepoint of this theory for infinite $N$ in the case of a quadratic scalar potential. I discuss some aspects of this solution and also show how the continuum D=1 matrix model with an arbitrary potential can be reproduced through this approach.

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