Antal Jevicki

Operator formulation of interacting string field theory (II)

Abstract The operator construction of the interacting string field theory presented by Witten is completed. The ghost sector of the theory is discussed in detail, using the fermionic formulation of the ghosts. The Fock space representation of the functionals that represent integration, multiplication, and the interaction vertex are constructed explicitly. We prove that the formalism is invariant under reparameterizations and under BRST gauge transformation.

The quantum collective field method and its application to the planar limit

Abstract We formulate a general method of collective fields in quantum theory, which represents a direct generalization of the Bohm-Pines treatment of plasma oscillations. The present method provides a complete procedure for reformulating a given quantum system in terms of a most general (overcomplete) set of commuting operators. We point out and exemplify how this formalism offers a new powerful method for studying the large- N limit. For illustration we discuss the collective motions of N identical harmonic oscillators. As a much more important application, we show how, based on the present formalism, one solves the planar limit of a non-trivial SU( N ) symmetric quantum theory.

Generating AdS string solutions

We use a Pohlmeyer type reduction to generate classical string solutions in AdS spacetime. In this framework we describe a correspondence between spikes in AdS3 and soliton profiles of the sinh-Gordon equation. The null cusp string solution and its closed spinning string counterpart are related to the sinh-Gordon vacuum. We construct classical string solutions corresponding to sinh-Gordon solitons, antisolitons and breathers by the inverse scattering technique. The breather solutions can also be reproduced by the sigma model dressing method.

Bi-local holography in the SYK model

A bstractWe discuss large N rules of the Sachdev-Ye-Kitaev model and the bi-local representation of holography of this theory. This is done by establishing 1/N Feynman rules in terms of bi-local propagators and vertices, which can be evaluated following the recent procedure of Polchinski and Rosenhaus. These rules can be interpreted as Witten type diagrams of the dual AdS theory, which we are able to define at IR fixed point and off.

Vibration modes of giant gravitons

We examine the spectrum of small vibrations of giant gravitons when the gravitons expand in anti\char21{}de Sitter space and when they expand on the sphere. For any given angular harmonic, the modes are found to have frequencies related to the curvature length scale of the background; these frequencies are independent of radius (and hence angular momentum) of the brane itself. This implies that the holographic dual theory must have, in a given R charge sector, low-lying non-BPS excitations with level spacings independent of the R charge.

Evaluation of glueball masses from supergravity

In the framework of the conjectured duality relation between large {ital N} gauge theory and supergravity the spectra of masses in large {ital N} gauge theory can be determined by solving certain eigenvalue problems in supergravity. In this paper we study the eigenmass problem given by Witten as a possible approximation for masses in QCD without supersymmetry. We place a particular emphasis on the treatment of the horizon and related boundary conditions. We construct exact expressions for the analytic expansions of the wave functions both at the horizon and at infinity and show that requiring smoothness at the horizon and normalizability gives a well defined eigenvalue problem. We show, for example, that there are no smooth solutions with a vanishing derivative at the horizon. The mass eigenvalues up to m{sup 2}=1000 corresponding to smooth normalizable wave functions are presented. We comment on the relation of our work with the results found in a recent paper by C. Cs{acute a}ki {ital et al.}, hep-th/9806021, which addresses the same problem. {copyright} {ital 1998} {ital The American Physical Society}

Lumps and p branes in open string field theory

Abstract We describe numerical methods for constructing lump solutions in open string field theory. According to Sen, these lumps represent lower dimensional Dp branes and numerical evaluation of their energy can be compared with the expected value for the tension. We take particular care of all higher derivative terms inherent in Wittens version of open string field theory. The importance of these terms for off shell phenomena is argued in the text. Detailed numerical calculations done for the case of general p brane show very good agreement with Sens conjectured value. This gives credence to the conjecture itself and establishes further the usefulness of Wittens version of SFT.

Classical integrability and higher symmetries of collective string field theory

Abstract We demonstrate the complete integrability of classical collective field theory. An exact equivalence to the classical N -body problem of Calogero type is described. A Lax pair is constructed for the general continuum collective equations. A form of background independence is pointed out. An infinite set of commuting currents is constructed in the general case. A large symmetry algebra is discovered and shown to take the form of a W ∞ algebra.

Collective field approach to the large-N limit: Euclidean field theories

Abstract We apply the collective field method to study the large-N behavior of euclidean field theories. We show how this method leads to an effective action whose stationary points determine the N → ∞ limit. This approach applies to Yang-Mills gauge theories and the effective action is given in terms of gauge-invariant Wilson loop variables.

Large- N collective fields and holography

We propose that the Euclidean bilocal collective field theory of critical large-N vector models provides a complete definition of the proposed dual theory of higher spin fields in anti\char21{}de Sitter spaces. We show how this bilocal field can be decomposed into an infinite number of even spin fields in one more dimension. The collective field has a nontrivial classical solution which leads to an