60 research outputs found
Stochastic quantization and holographic Wilsonian renormalization group
We study relation between stochastic quantization and holographic Wilsonian
renormalization group flow. Considering stochastic quantization of the boundary
on-shell actions with the Dirichlet boundary condition for certain bulk
gravity theories, we find that the radial flows of double trace deformations in
the boundary effective actions are completely captured by stochastic time
evolution with identification of the radial coordinate `' with the
stochastic time '' as . More precisely, we investigate Langevin
dynamics and find an exact relation between radial flow of the double trace
couplings and 2-point correlation functions in stochastic quantization. We also
show that the radial evolution of double trace deformations in the boundary
effective action and the stochastic time evolution of the Fokker-Planck action
are the same. We demonstrate this relation with a couple of examples:
(minimally coupled)massless scalar fields in and U(1) vector fields in
.Comment: 1+30 pages, a new subsection is added, references are adde
BKM Lie superalgebra for the Z_5 orbifolded CHL string
We study the Z_5-orbifolding of the CHL string theory by explicitly
constructing the modular form tilde{Phi}_2 generating the degeneracies of the
1/4-BPS states in the theory. Since the additive seed for the sum form is a
weak Jacobi form in this case, a mismatch is found between the modular forms
generated from the additive lift and the product form derived from threshold
corrections. We also construct the BKM Lie superalgebra, tilde{G}_5,
corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2}
which happens to be a hyperbolic algebra. This is the first occurrence of a
hyperbolic BKM Lie superalgebra. We also study the walls of marginal stability
of this theory in detail, and extend the arithmetic structure found by Cheng
and Dabholkar for the N=1,2,3 orbifoldings to the N=4,5 and 6 models, all of
which have an infinite number of walls in the fundamental domain. We find that
analogous to the Stern-Brocot tree, which generated the intercepts of the walls
on the real line, the intercepts for the N >3 cases are generated by linear
recurrence relations. Using the correspondence between the walls of marginal
stability and the walls of the Weyl chamber of the corresponding BKM Lie
superalgebra, we propose the Cartan matrices for the BKM Lie superalgebras
corresponding to the N=5 and 6 models.Comment: 30 pages, 2 figure
BPS black holes, the Hesse potential, and the topological string
The Hesse potential is constructed for a class of four-dimensional N=2
supersymmetric effective actions with S- and T-duality by performing the
relevant Legendre transform by iteration. It is a function of fields that
transform under duality according to an arithmetic subgroup of the classical
dualities reflecting the monodromies of the underlying string compactification.
These transformations are not subject to corrections, unlike the
transformations of the fields that appear in the effective action which are
affected by the presence of higher-derivative couplings. The class of actions
that are considered includes those of the FHSV and the STU model. We also
consider heterotic N=4 supersymmetric compactifications. The Hesse potential,
which is equal to the free energy function for BPS black holes, is manifestly
duality invariant. Generically it can be expanded in terms of powers of the
modulus that represents the inverse topological string coupling constant,
, and its complex conjugate. The terms depending holomorphically on
are expected to correspond to the topological string partition function and
this expectation is explicitly verified in two cases. Terms proportional to
mixed powers of and are in principle present.Comment: 28 pages, LaTeX, added comment
BKM Lie superalgebras from counting twisted CHL dyons
Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS
states that contribute to twisted helicity trace indices in four-dimensional
CHL models with N=4 supersymmetry. The generating functions of half-BPS states,
twisted as well as untwisted, are given in terms of multiplicative eta products
with the Mathieu group, M_{24}, playing an important role. These multiplicative
eta products enable us to construct Siegel modular forms that count twisted
quarter-BPS states. The square-roots of these Siegel modular forms turn out be
precisely a special class of Siegel modular forms, the dd-modular forms, that
have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each
one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator
formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the
Weyl chamber are in one-to-one correspondence with the walls of marginal
stability in the corresponding CHL model for twisted dyons as well as untwisted
ones. This leads to a periodic table of BKM Lie superalgebras with properties
that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio
BPS black holes in N=2 D=4 gauged supergravities
We construct and analyze BPS black hole solutions in gauged N=2, D=4
supergravity with charged hypermultiplets. A class of solutions can be found
through spontaneous symmetry breaking in vacua that preserve maximal
supersymmetry. The resulting black holes do not carry any hair for the scalars.
We demonstrate this with explicit examples of both asymptotically flat and
anti-de Sitter black holes. Next, we analyze the BPS conditions for
asymptotically flat black holes with scalar hair and spherical or axial
symmetry. We find solutions only in cases when the metric contains ripples and
the vector multiplet scalars become ghost-like. We give explicit examples that
can be analyzed numerically. Finally, we comment on a way to circumvent the
ghost-problem by introducing also fermionic hair.Comment: 40 pages, 2 figures; v2 references added; v3 minor changes, published
versio
Massive Gravity Theories and limits of Ghost-free Bigravity models
We construct a class of theories which extend New Massive Gravity to higher
orders in curvature in any dimension. The lagrangians arise as limits of a new
class of bimetric theories of Lovelock gravity, which are unitary theories free
from the Boulware-Deser ghost. These Lovelock bigravity models represent the
most general non-chiral ghost-free theories of an interacting massless and
massive spin-two field in any dimension. The scaling limit is taken in such a
way that unitarity is explicitly broken, but the Boulware-Deser ghost remains
absent. This automatically implies the existence of a holographic -theorem
for these theories. We also show that the Born-Infeld extension of New Massive
Gravity falls into our class of models demonstrating that this theory is also
free of the Boulware-Deser ghost. These results extend existing connections
between New Massive Gravity, bigravity theories, Galileon theories and
holographic -theorems.Comment: 11+5 page
No entropy enigmas for N=4 dyons
We explain why multi-centered black hole configurations where at least one of
the centers is a large black hole do not contribute to the indexed degeneracies
in theories with N=4 supersymmetry. This is a consequence of the fact that such
configurations, although supersymmetric, belong to long supermultiplets. As a
result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.Comment: 14 page
Counting all dyons in N =4 string theory
For dyons in heterotic string theory compactified on a six-torus, with
electric charge vector Q and magnetic charge vector P, the positive integer I =
g.c.d.(Q \wedge P) is an invariant of the U-duality group. We propose the
microscopic theory for computing the spectrum of all dyons for all values of I,
generalizing earlier results that exist only for the simplest case of I=1. Our
derivation uses a combination of arguments from duality, 4d-5d lift, and a
careful analysis of fermionic zero modes. The resulting degeneracy agrees with
the black hole degeneracy for large charges and with the degeneracy of
field-theory dyons for small charges. It naturally satisfies several physical
requirements including integrality and duality invariance. As a byproduct, we
also derive the microscopic (0,4) superconformal field theory relevant for
computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE
backgrounds and count the resulting degeneracies
Discrete Information from CHL Black Holes
AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index
over states carrying a fixed set of charges grows as 1/N times the entropy of
the black hole carrying the same set of charges. In this paper we verify this
explicitly by calculating the microscopic Z_N twisted index for a class of
states in the CHL models. This demonstrates that black holes carry more
information about the microstates than just the total degeneracy.Comment: LaTeX file, 24 pages; v2: references adde
Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
In order to understand thermodynamical properties of N D-branes with chemical
potentials associated with R-symmetry charges, we study a one dimensional large
N gauge theory (bosonic BFSS type model) as a first step. This model is
obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills
theory and we use a 1/D expansion to investigate the phase structure. We find
three phases in the \mu-T plane. We also show that all the adjoint scalars
condense at large D and obtain a mass dynamically. This dynamical mass protects
our model from the usual perturbative instability of massless scalars in a
non-zero chemical potential. We find that the system is at least meta-stable
for arbitrary large values of the chemical potentials in D \to \infty limit. We
also explore the existence of similar condensation in higher dimensional gauge
theories in a high temperature limit. In 2 and 3 dimensions, the condensation
always happens as in one dimensional case. On the other hand, if the dimension
is higher than 4, there is a critical chemical potential and the condensation
happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3:
minor corrections, to appear in JHE
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