290 research outputs found
Axion-Dilaton Domain Walls and Fake Supergravity
Dynamical systems methods are used to investigate domain-wall solutions of a
two-parameter family of models in which gravity is coupled to an axion, and to
a dilaton with an exponential potential of either sign. A complete global
analysis is presented for (i) constant axion and (ii) flat walls, including a
study of bifurcations and a new exact domain-wall solution with non-constant
axion. We reconsider `fake supergravity' issues in light of these results. We
show, by example, how domain walls determine multi-valued superpotentials that
branch at stationary points that are not stationary points of the potential,
and we apply this result to potentials with anti-de Sitter vacua. We also show
by example that `adapted' truncation to a single-scalar model is sometimes
inconsistent, and we propose a `generalized' fake supergravity formalism that
applies in some such cases.Comment: 43pp, 19 figures; minor corrections and extensions; one additional
figur
Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence
The correspondence between domain-wall and cosmological solutions of gravity
coupled to scalar fields is explained. Any domain wall solution that admits a
Killing spinor is shown to correspond to a cosmology that admits a
pseudo-Killing spinor: whereas the Killing spinor obeys a Dirac-type equation
with hermitian `mass'-matrix, the corresponding pseudo-Killing spinor obeys a
Dirac-type equation with a anti-hermitian `mass'-matrix. We comment on some
implications of (pseudo)supersymmetry.Comment: 11 pages, contribution to the proceedings of IRGAC 2006;v3: minor
change
The Geometric Phase and Gravitational Precession of D-Branes
We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in
the background of D4-branes, the first excited states undergo a holonomy
described by a non-Abelian Berry connection. At weak coupling this is an SU(2)
connection over R^5, known as the Yang monopole. At strong coupling, the
holonomy is recast as the classical gravitational precession of a spinning
particle. The Berry connection is the spin connection of the near-horizon limit
of the D4-branes, which is a continuous deformation of the Yang and anti-Yang
monopole.Comment: 23 pages; v3: typos correcte
On the positivity of solutions of systems of stochastic PDEs
We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit necessary and sufficient conditions such that the solutions preserve positivity. These conditions imply the positivity of the solutions of the stochastic system for both Itô's and Stratonovich's interpretation of stochastic differential equations. We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit necessary and sufficient conditions such that the solutions preserve positivity. These conditions imply the positivity of the solutions of the stochastic system for both Itô's and Stratonovich's interpretation of stochastic differential equations
From Wave Geometry to Fake Supergravity
The `Wave Geometry' equation of the pre-WWII Hiroshima program is also the
key equation of the current `fake supergravity' program. I review the status of
(fake) supersymmetric domain walls and (fake) pseudo-supersymmetric
cosmologies. An extension of the domain-wall/cosmology correspondence to a
triple correspondence with instantons shows that `pseudo-supersymmetry' has
another interpretation as Euclidean supersymmetry.Comment: 14 pages. Minor Revisions to original. To appear in proceedings of
the 5th International Symposium on Quantum Theory and Symmetries (QTS5),
Vallodolid, July 2007. in version
Domain-wall/Cosmology correspondence in adS/dS supergravity
We realize the domain-wall/cosmology correspondence for
(pseudo)supersymmetric domain walls (cosmologies) in the context of
four-dimensional supergravity. The OSp(2|4)-invariant anti-de Sitter (adS)
vacuum of a particular N=2 Maxwell-Einstein supergravity theory is shown to
correspond to the OSp(2^*|2,2)-invariant de Sitter (dS) vacuum of a particular
pseudo-supergravity model, with `twisted' reality conditions on spinors. More
generally, supersymmetric domain walls of the former model correspond to
pseudo-supersymmetric cosmologies of the latter model, with time-dependent
pseudo-Killing spinors that we give explicitly.Comment: 21 pages;v2: rewritten to clarify the link with fake supergravity --
main results unchanged; v3: typos corrected, two refs added, JHEP versio
A bulk manifestation of Krylov complexity
There are various definitions of the concept of complexity in Quantum Field
Theory as well as for finite quantum systems. For several of them there are
conjectured holographic bulk duals. In this work we establish an entry in the
AdS/CFT dictionary for one such class of complexity, namely Krylov or
K-complexity. For this purpose we work in the double-scaled SYK model which is
dual in a certain limit to JT gravity, a theory of gravity in AdS. In
particular, states on the boundary have a clear geometrical definition in the
bulk. We use this result to show that Krylov complexity of the
infinite-temperature thermofield double state on the boundary of AdS has a
precise bulk description in JT gravity, namely the length of the two-sided
wormhole. We do this by showing that the Krylov basis elements, which are
eigenstates of the Krylov complexity operator, are mapped to length eigenstates
in the bulk theory by subjecting K-complexity to the bulk-boundary map
identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of
chord diagram techniques and identifies the Krylov basis of the boundary
quantum system with fixed chord number states building the bulk gravitational
Hilbert space.Comment: v1: 37 pages + appendices, 12 figures. v2: published versio
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