Brane Waves, Yang-Mills theories and Causality

We provide evidence for the validity of AdS/CFT correspondence in the Coulomb branch by comparing the Yang-Mills effective action with the potential between waves on two separated test 3-branes in the presence of a large number of other 3-branes. For constant gauge fields excited on the branes, this requires that the supergravity potential in a $AdS_5 \times S^5$ background is the {\it same} as that in flat space, despite the fact that both propagators and couplings of some relevant supergravity modes are different. We show that this is indeed true, due to a subtle cancellation. With time-dependent gauge fields on the test branes, the potential is sensitive to retardation effects of causal propagation in the bulk. We argue that this is reflected in higher derivative (acceleration) terms in the Yang-Mills effective action. We show that for two 3-branes separated in flat space the structure of lowest order acceleration terms is in agreement with supergravity expectations.Comment: 20 pages, harvmac, references adde

D branes in 2d String Theory and Classical limits

In the matrix model formulation of two dimensional noncritical string theory, a D0 brane is identified with a single eigenvalue excitation. In terms of open string quantities (i.e fermionic eigenvalues) the classical limit of a macroscopically large number of D0 branes has a smooth classical limit : they are described by a filled region of phase space whose size is O(1) and disconnected from the Fermi sea. We show that while this has a proper description in terms of a {\em single} bosonic field at the quantum level, the classical limit is rather nontrivial. The quantum dispersions of bosonic quantities {\em survive in the classical limit} and appear as additional fields in a semiclassical description. This reinforces the fact that while the open string field theory description of these D-branes (i.e. in terms of fermions) has a smooth classical limit, a closed string field theory description (in terms of a single boson) does not.Comment: LaTeX, 17 pages, 3 .eps figures, based on talks at "QTS3" at Cincinnati and "Workshop on Branes" at Argonn

Holograms of Branes in the Bulk and Acceleration Terms in SYM Effective Action

If the AdS/CFT correspondence is valid in the Coulomb branch, the potential between waves on a pair of test branes in the bulk should be reproduced by the relevant Yang-Mills theory effective action on the boundary. Earlier work has provided evidence for this in the case of constant gauge field brane waves. In this paper we provide concrete evidence for an earlier proposal that the effects of exchange of supergravity modes with nonzero momentum in the brane directions are encoded in certain terms involving derivatives of the field strength in the gauge theory effective action. We explicitly calculate the force quadratic in the field strengths coming from the exchange of non-zero momentum two form fields between two 3-branes in $AdS_5 \times S^5$ to lowest nontrivial order in the momentum. We show that this is exactly the same as that between the branes living in flat space. The result is in agreement with the gauge theory effective action and consistent with the non-renormalization property of this term. We comment on the relationship of other ``acceleration'' terms in the SYM effective action with quantities in supergravity.Comment: 16 pages, harvmac, typos corrected, comments adde

Matrix Models and Nonperturbative String Propagation in Two-Dimensional Black Hole Backgrounds

We identify a quantity in the $c=1$ matrix model which describes the wavefunction for physical scattering of a tachyon from a black hole of the two dimensional critical string theory. At the semiclassical level this quantity corresponds to the usual picture of a wave coming in from infinity, part of which enters the black hole becoming singular at the singularity, while the rest is scattered back to infinity, with nothing emerging from the whitehole. We find, however, that the exact nonperturbative wavefunction is nonsingular at the singularity and appears to end up in the asymptotic region ``behind'' the singularity.Comment: 14 pages, phyzzx, EFI-93-1

Realizations of Conformal and Heisenberg Algebras in PP-wave-CFT Correspondence

We elaborate on the symmetry breaking pattern involved in the Penrose limit of $AdS_{d+1} \times S^{d+1}$ spacetimes and the corresponding limit of the CFT dual. For d=2 we examine in detail how the symmetries contract to products of rotation and Heisenberg algebras, both from the bulk and CFT points of view. Using a free field realization of these algebras acting on products of elementary fields of the CFT with SO(2) R charge +1, we show that this process of contraction restricts all the fields to a few low angular momentum modes and ensures that the field with R charge -1 does not appear. This provides an understanding of several important aspects of the proposal of Berenstein, Maldacena and Nastase. We also indicate how the contraction can be performed on correlation functions.Comment: 24 pages, LaTe

Kibble-Zurek Scaling in Holographic Quantum Quench : Backreaction

We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.1776) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any self-coupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor.Comment: 25 pages; v2 minor corrections; v3 minor corrections, to appear in JHE