576 research outputs found
Quantum Mechanics, Random Matrices and BMN Gauge Theory
We review how the identification of gauge theory operators representing
string states in the pp-wave/BMN correspondence and their associated anomalous
dimension reduces to the determination of the eigenvectors and the eigenvalues
of a simple quantum mechanical Hamiltonian and analyze the properties of this
Hamiltonian. Furthermore, we discuss the role of random matrices as a tool for
performing explicit evaluation of correlation functions.Comment: 16 pages, contribution to proceedings of Workshop on Random Geometry,
Krakow, May, 200
Giant D5 Brane Holographic Hall State
We find a new holographic description of strongly coupled defect field
theories using probe D5 branes. We consider a system where a large number of
probe branes, which are asymptotically D5 branes, blow up into a D7 brane
suspended in the bulk of anti-de Sitter space. For a particular ratio of charge
density to external magnetic field, so that the Landau level filling fraction
per color is equal to one, the D7 brane exhibits an incompressible
charge-gapped state with one unit of integer quantized Hall conductivity. The
detailed configuration as well as ungapped, compressible configurations for a
range of parameters near the gapped one are found by solving the D5 and D7
brane embedding equations numerically and the D7 is shown to be preferred over
the D5 by comparing their energies. We then find integer quantum Hall states
with higher filling fractions as a stack of D5 branes which blow up to multiple
D7 branes where each D7 brane has filling fraction one. We find indications
that the n D7 branes describing the filling fraction n state are coincident
with a residual SU(n) symmetry when n is a divisor of the total number of D5
branes. We examine the issue of stability of the larger filling fraction Hall
states. We argue that, in the D7 brane phase, chiral symmetry restoration could
be a first order phase transition.Comment: 30 pages, 15 figures, typos fixed, some clarifying comments adde
The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
Using the quantum string Bethe ansatz we derive the one-loop energy of a
folded string rotating with angular momenta (S,J) in AdS_3 x S^1 inside AdS_5 x
S^5 in the limit 1 << J << S, z=\lambda^(1/2) log(S/J) /(\pi J) fixed. The
one-loop energy is a sum of two contributions, one originating from the
Hernandez-Lopez phase and another one being due to spin chain finite size
effects. We find a result which at the functional level exactly matches the
result of a string theory computation. Expanding the result for large z we
obtain the strong coupling limit of the scaling function for low twist, high
spin operators of the SL(2) sector of N=4 SYM. In particular we recover the
famous -3 log(2)/\pi. Its appearance is a result of non-trivial cancellations
between the finite size effects and the Hernandez-Lopez correction.Comment: 18 pages, one figure, v2: footnote changed, v3: reference added, typo
correcte
From 1-matrix model to Kontsevich model
Loop equations of matrix models express the invariance of the models under
field redefinitions. We use loop equations to prove that it is possible to
define continuum times for the generic hermitian {1-matrix} model such that all
correlation functions in the double scaling limit agree with the corresponding
correlation functions of the Kontsevich model expressed in terms of kdV times.
In addition the double scaling limit of the partition function of the hermitian
matrix model agree with the -function of the kdV hierarchy corresponding
to the Kontsevich model (and not the square of the -function) except for
some complications at genus zero.Comment: 17 pages, Late
Integrable boundary states in D3-D5 dCFT: beyond scalars
A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the
gauge group jumps by k units across a domain wall. The one-point functions of
local operators in this set-up map to overlaps between on-shell Bethe states in
the underlying spin chain and a boundary state representing the D5 brane.
Focussing on the k=1 case, we extend the construction to gluonic and fermionic
sectors, which was prohibitively difficult to achieve for k>1. As a byproduct,
we test an all-loop proposal for the one-point functions in the su(2) sector at
the half-wrapping order of perturbation theory.Comment: 30 pages, 3 figures; v2: distinction between asymptotic and wrapping
contributions clarifie
On the Regularization of Extremal Three-point Functions Involving Giant Gravitons
In the AdS_5/CFT_4 set-up, extremal three-point functions involving two giant
1/2 BPS gravitons and one point-like 1/2 BPS graviton, when calculated using
semi-classical string theory methods, match the corresponding three-point
functions obtained in the tree-level gauge theory. The string theory
computation relies on a certain regularization procedure whose justification is
based on the match between gauge and string theory. We revisit the
regularization procedure and reformulate it in a way which allows a
generalization to the ABJM set-up where three-point functions of 1/2 BPS
operators are not protected and where a match between tree-level gauge theory
and semi-classical string theory is hence not expected.Comment: 5 pages, no figures. v2 updated reference
One-point Functions in Defect CFT and Integrability
We calculate planar tree level one-point functions of non-protected operators
in the defect conformal field theory dual to the D3-D5 brane system with k
units of the world volume flux. Working in the operator basis of Bethe
eigenstates of the Heisenberg XXX_{1/2} spin chain we express the one-point
functions as overlaps of these eigenstates with a matrix product state. For k=2
we obtain a closed expression of determinant form for any number of
excitations, and in the case of half-filling we find a relation with the N\'eel
state. In addition, we present a number of results for the limiting case of
infinite k.Comment: 31 pages, 3 figures; v2: references adde
One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT
We study tree level one-point functions of non-protected scalar operators in
the defect CFT, based on N=4 SYM, which is dual to the SO(5) symmetric D3-D7
probe brane system with non-vanishing instanton number. Whereas symmetries
prevent operators from the SU(2) and SU(3) sub-sectors from having
non-vanishing one-point functions, more general scalar conformal operators,
which in particular constitute Bethe eigenstates of the integrable SO(6) spin
chain, are allowed to have non-trivial one-point functions. For a series of
operators with a small number of excitations we find closed expressions in
terms of Bethe roots for these one-point functions, valid for any value of the
instanton number. In addition, we present some numerical results for operators
with more excitations.Comment: 15 pages, 1 figure. Minor corrections & update
Wilson lines in AdS/dCFT
We consider the expectation value of Wilson lines in two defect versions of N
= 4 SYM, both with supersymmetry completely broken, where one is described in
terms of an integrable boundary state, the other one not. For both cases,
imposing a certain double scaling limit, we find agreement to two leading
orders between the expectation values calculated from respectively the field
theory and the string theory side of the AdS/dCFT correspondence.Comment: 8 pages, 2 figures; typos correcte
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