5,345 research outputs found
Holographic Renormalization of general dilaton-axion gravity
We consider a very general dilaton-axion system coupled to Einstein-Hilbert
gravity in arbitrary dimension and we carry out holographic renormalization for
any dimension up to and including five dimensions. This is achieved by
developing a new systematic algorithm for iteratively solving the radial
Hamilton-Jacobi equation in a derivative expansion. The boundary term derived
is valid not only for asymptotically AdS backgrounds, but also for more general
asymptotics, including non-conformal branes and Improved Holographic QCD. In
the second half of the paper, we apply the general result to Improved
Holographic QCD with arbitrary dilaton potential. In particular, we derive the
generalized Fefferman-Graham asymptotic expansions and provide a proof of the
holographic Ward identities.Comment: 42 pages. v2: two references added. Version published in JHEP. v3:
fixed minor typos in eqs. (1.6), (2.3), (3.20), (A.3), (B.8), (B.12) and
(B.22
Positivity of energy for asymptotically locally AdS spacetimes
We derive necessary conditions for the spinorial Witten-Nester energy to be
well-defined for asymptotically locally AdS spacetimes. We find that the
conformal boundary should admit a spinor satisfying certain differential
conditions and in odd dimensions the boundary metric should be conformally
Einstein. We show that these conditions are satisfied by asymptotically AdS
spacetimes. The gravitational energy (obtained using the holographic stress
energy tensor) and the spinorial energy are equal in even dimensions and differ
by a bounded quantity related to the conformal anomaly in odd dimensions.Comment: 36 pages, 1 figure; minor corrections, JHEP versio
Hamilton-Jacobi method for Domain Walls and Cosmologies
We use Hamiltonian methods to study curved domain walls and cosmologies. This
leads naturally to first order equations for all domain walls and cosmologies
foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain
walls (flat and closed FLRW cosmologies) we recover a recent result concerning
their (pseudo)supersymmetry. We show how domain-wall stability is consistent
with the instability of adS vacua that violate the Breitenlohner-Freedman
bound. We also explore the relationship to Hamilton-Jacobi theory and compute
the wave-function of a 3-dimensional closed universe evolving towards de Sitter
spacetime.Comment: 18 pages; v2: typos corrected, one ref added, version to appear in
PR
First Law, Counterterms and Kerr-AdS_5 Black Holes
We apply the counterterm subtraction technique to calculate the action and
other quantities for the Kerr--AdS black hole in five dimensions using two
boundary metrics; the Einstein universe and rotating Einstein universe with
arbitrary angular velocity. In both cases, the resulting thermodynamic
quantities satisfy the first law of thermodynamics. We point out that the
reason for the violation of the first law in previous calculations is that the
rotating Einstein universe, used as a boundary metric, was rotating with an
angular velocity that depends on the black hole rotation parameter. Using a new
coordinate system with a boundary metric that has an arbitrary angular
velocity, one can show that the resulting physical quantities satisfy the first
law.Comment: 19 pages, 1 figur
Anatomy of bubbling solutions
We present a comprehensive analysis of holography for the bubbling solutions
of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring
of a 2-plane, which was argued to correspond to the phase space of free
fermions. We show that in general this phase space distribution does not
determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is
dual to, but it does determine it enough so that vevs of all single trace 1/2
BPS operators in that state are uniquely determined to leading order in the
large N limit. These are precisely the vevs encoded in the asymptotics of the
LLM solutions. We extract these vevs for operators up to dimension 4 using
holographic renormalization and KK holography and show exact agreement with the
field theory expressions.Comment: 67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded
explanations, more typos correcte
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
The holographic quantum effective potential at finite temperature and density
We develop a formalism that allows the computation of the quantum effective
potential of a scalar order parameter in a class of holographic theories at
finite temperature and charge density. The effective potential is a valuable
tool for studying the ground state of the theory, symmetry breaking patterns
and phase transitions. We derive general formulae for the effective potential
and apply them to determine the phase transition temperature and density in the
scaling region.Comment: 27 page
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