255 research outputs found
Thermodynamics of Dyonic Lifshitz Black Holes
Black holes with asymptotic anisotropic scaling are conjectured to be gravity
duals of condensed matter system close to quantum critical points with
non-trivial dynamical exponent z at finite temperature. A holographic
renormalization procedure is presented that allows thermodynamic potentials to
be defined for objects with both electric and magnetic charge in such a way
that standard thermodynamic relations hold. Black holes in asymptotic Lifshitz
spacetimes can exhibit paramagnetic behavior at low temperature limit for
certain values of the critical exponent z, whereas the behavior of AdS black
holes is always diamagnetic.Comment: 26 pages, 4 figure
Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities
We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite
temperature with nonzero R-charge densities, and in Non-Commutative gauge
theory at finite temperature. The gluon scattering amplitude is defined as a
light-like Wilson loop which lives at the horizon of the T-dual black holes of
the backgrounds we consider. We study in detail a special amplitude, which
corresponds to forward scattering of a low energy gluon off a high energy one.
For this kinematic configuration in the considered backgrounds, we find the
corresponding minimal surface which is directly related to the gluon scattering
amplitude. We find that for increasing the chemical potential or the
non-commutative parameter, the on-shell action corresponding to our Wilson loop
in the T-dual space decreases. For all of our solutions the length of the short
side of the Wilson loop is constrained by an upper bound which depends on the
temperature, the R-charge density and the non-commutative parameter. Due to
this constraint, in the limit of zeroth temperature our approach breaks down
since the upper bound goes to zero, while by keeping the temperature finite and
letting the chemical potential or the non-commutative parameter to approach to
zero the limit is smooth.Comment: 30 pages, 16 figures, minor corrections (plus improved numerical
computation for the non-commutative case
Unraveling L_{n,k}: Grassmannian Kinematics
It was recently proposed that the leading singularities of the S-Matrix of N
= 4 super Yang-Mills theory arise as the residues of a contour integral over a
Grassmannian manifold, with space-time locality encoded through residue
theorems generalizing Cauchy's theorem to more than one variable. We provide a
method to identify the residue corresponding to any leading singularity, and we
carry this out very explicitly for all leading singularities at tree level and
one-loop. We also give several examples at higher loops, including all generic
two-loop leading singularities and an interesting four-loop object. As a
special case we consider a 12-pt N^4MHV leading singularity at two loops that
has a new kinematic structure involving double square roots. Our analysis
results in a simple picture for how the topological structure of loop graphs is
reflected in various substructures within the Grassmannian.Comment: 26+11 page
Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
We study classical open string solutions with a null polygonal boundary in
AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at
strong coupling. We derive in full detail the set of integral equations
governing the decagonal and the dodecagonal solutions and identify them with
the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models.
By evaluating the free energy in the conformal limit we compute the central
charges, from which we observe general correspondence between the polygonal
solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor
corrections, v3: references added, minor corrections, to appear in JHE
The S-Matrix in Twistor Space
The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity
scattering amplitudes suggest the existence of a "weak-weak" dual formulation
in which these structures are made manifest at the expense of manifest
locality. We suggest that this dual description lives in (2,2) signature and is
naturally formulated in twistor space. We recast the BCFW recursion relations
in an on-shell form that begs to be transformed into twistor space. Our twistor
transformation is inspired by Witten's, but differs in treating twistor and
dual twistor variables more equally. In these variables the three and
four-point amplitudes are amazingly simple; the BCFW relations are represented
by diagrammatic rules that precisely define the "twistor diagrams" of Andrew
Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees;
they reveal striking connections between amplitudes and suggest a new form for
them in momentum space. We also obtain a twistorial formulation of gravity. All
tree amplitudes can be combined into an "S-Matrix" functional which is the
natural holographic observable in asymptotically flat space; the BCFW formula
turns into a quadratic equation for this "S-Matrix", providing a holographic
description of N=4 SYM and N=8 Supergravity at tree level. We explore loop
amplitudes in (2,2) signature and twistor space, beginning with a discussion of
IR behavior. We find that the natural pole prescription renders the amplitudes
well-defined and free of IR divergences. Loop amplitudes vanish for generic
momenta, and in twistor space are even simpler than their tree-level
counterparts! This further supports the idea that there exists a sharply
defined object corresponding to the S-Matrix in (2,2) signature, computed by a
dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of
the paper. V2: 49 pages + 24 figures. Largely expanded set of references
included. Some diagrammatic clarifications added, minor typo fixe
The particle number in Galilean holography
Recently, gravity duals for certain Galilean-invariant conformal field
theories have been constructed. In this paper, we point out that the spectrum
of the particle number operator in the examples found so far is not a necessary
consequence of the existence of a gravity dual. We record some progress towards
more realistic spectra. In particular, we construct bulk systems with
asymptotic Schrodinger symmetry and only one extra dimension. In examples, we
find solutions which describe these Schrodinger-symmetric systems at finite
density. A lift to M-theory is used to resolve a curvature singularity. As a
happy byproduct of this analysis, we realize a state which could be called a
holographic Mott insulator.Comment: 29 pages, 1 rudimentary figure; v2: typo in eqn (3.4), added comments
and ref
Wilson Loop Renormalization Group Flows
The locally BPS Wilson loop and the pure gauge Wilson loop map under AdS/CFT
duality to string world-sheet boundaries with standard and alternate
quantizations of the world-sheet fields. This implies an RG flow between the
two operators, which we verify at weak coupling. Many additional loop operators
exist at strong coupling, with a rich pattern of RG flows.Comment: 10 p, 2 figures. v3: Title change, expanded treatment of RG flow
Flavor-symmetry Breaking with Charged Probes
We discuss the recombination of brane/anti-brane pairs carrying brane
charge in . These configurations are dual to co-dimension one
defects in the super-Yang-Mills description. Due to their
charge, these defects are actually domain walls in the dual gauge theory,
interpolating between vacua of different gauge symmetry. A pair of unjoined
defects each carry localized dimensional fermions and possess a global
flavor symmetry while the recombined brane/anti-brane pairs
exhibit only a diagonal U(N). We study the thermodynamics of this
flavor-symmetry breaking under the influence of external magnetic field.Comment: 21 pages, 10 figure
Holographic Symmetry-Breaking Phases in AdS/CFT
In this note we study the symmetry-breaking phases of 3D gravity coupled to
matter. In particular, we consider black holes with scalar hair as a model of
symmetry-breaking phases of a strongly coupled 1+1 dimensional CFT. In the case
of a discrete symmetry, we show that these theories admit metastable phases of
broken symmetry and study the thermodynamics of these phases. We also
demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry
breaking at low temperature. The apparent contradiction with the
Coleman-Mermin-Wagner theorem is discussed.Comment: 15 pages, 7 figur
Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes
We study the effect of an order N^2 density of heavy quarks in strongly
coupled N=4 SUSY Yang-Mills theory in the large N limit. This is achieved in
the type IIB supergravity dual by introducing a uniformly smeared density of
macroscopic string sources stretching to the boundary of AdS_5 x S^5. The
backreacted system exhibits a flow from an AdS_5 "hedgehog" geometry to a
scaling Lifshitz-like solution Lif_5 x S^5 with dynamical critical exponent
z=7, wherein the scaling symmetry is broken by a logarithmic running dilaton.
We find an exact black brane solution within the scaling regime which describes
the low temperature thermodynamics of the system.Comment: 20 pages, 2 figures, references adde
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