557 research outputs found
On Some Universal Features of the Holographic Quantum Complexity of Bulk Singularities
We perform a comparative study of the time dependence of the holographic
quantum complexity of some space like singular bulk gravitational backgrounds.
This is done by considering the two available notions of complexity, one that
relates it to the maximal spatial volume and the other that relates it to the
classical action of the Wheeler-de Witt patch. We calculate and compare the
leading and the next to leading terms and find some universal features. The
complexity decreases towards the singularity for both definitions, for all
types of singularities studied. In addition the leading terms have the same
quantitative behavior for both definitions in restricted number of cases and
the behaviour itself is different for different singular backgrounds. The
quantitative details of the next to leading terms, such as their specific form
of time dependence, are found not to be universal. They vary between the
different cases and between the different bulk definitions of complexity. We
also address some technical points inherent to the calculation.Comment: 24 pages, 6 figures. v2: minor correction
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
Strong coupling expansion of chiral models
A general precedure is outlined for an algorithmic implementation of the
strong coupling expansion of lattice chiral models on arbitrary lattices. A
symbolic character expansion in terms of connected values of group integrals on
skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9
On Thermodynamical Properties of Some Coset CFT Backgrounds
We investigate the thermodynamical features of two Lorentzian signature
backgrounds that arise in string theory as exact CFTs and possess more than two
disconnected asymptotic regions: the 2-d charged black hole and the
Nappi-Witten cosmological model. We find multiple smooth disconnected Euclidean
versions of the charged black hole background. They are characterized by
different temperatures and electro-chemical potentials. We show that there is
no straightforward analog of the Hartle-Hawking state that would express these
thermodynamical features. We also obtain multiple Euclidean versions of the
Nappi-Witten cosmological model and study their singularity structure. It
suggests to associate a non-isotropic temperature with this background.Comment: 1+39 pages, harvmac, 8 eps figure
Vacuum structure of CP^N sigma models at theta=pi
We show that parity symmetry is not spontaneously broken in the CP^N sigma
model for any value of N when the coefficient of the --term becomes
(mod ). The result follows from a non-perturbative analysis
of the nodal structure of the vacuum functional . The dynamical role
of sphalerons turns out to be very important for the argument. The result
introduces severe constraints on the possible critical behavior of the models
at (mod ).Comment: 8 pages, revtex, to appear in Phys. Rev. Let
Nonrigid chiral soliton for the octet and decuplet baryons
Systematic treatment of the collective rotation of the nonrigid chiral
soliton is developed in the SU(3) chiral quark soliton model and applied to the
octet and decuplet baryons. The strangeness degrees of freedom are treated by a
simplified bound-state approach which omits the locality of the kaon wave
function. Then, the flavor rotation is divided into the isospin rotation and
the emission and absorption of the kaon. The kaon Hamiltonian is diagonalized
by the Hartree approximation. The soliton changes the shape according to the
strangeness. The baryons appear as the rotational bands of the combined system
of the soliton and the kaon.Comment: 11 pages(LaTex), 1 figures(eps
Ricci flow and black holes
Gradient flow in a potential energy (or Euclidean action) landscape provides
a natural set of paths connecting different saddle points. We apply this method
to General Relativity, where gradient flow is Ricci flow, and focus on the
example of 4-dimensional Euclidean gravity with boundary S^1 x S^2,
representing the canonical ensemble for gravity in a box. At high temperature
the action has three saddle points: hot flat space and a large and small black
hole. Adding a time direction, these also give static 5-dimensional
Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action.
The small black hole has a Gross-Perry-Yaffe-type negative mode, and is
therefore unstable under Ricci flow. We numerically simulate the two flows
seeded by this mode, finding that they lead to the large black hole and to hot
flat space respectively, in the latter case via a topology-changing
singularity. In the context of string theory these flows are world-sheet
renormalization group trajectories. We also use them to construct a novel free
energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space
of metrics corrected and expanded, references adde
D-branes at multicritical points
The moduli space of c=1 conformal field theories in two dimensions has a
multicritical point, where a circle theory is equivalent to an orbifold theory.
We analyse all the conformal branes in both descriptions of this theory, and
find convincing evidence that the full brane spectrum coincides. This shows
that the equivalence of the two descriptions at this multicritical point
extends to the boundary sector. We also perform the analogous analysis for one
of the multicritical points of the N=1 superconformal field theories at c=3/2.
Again the brane spectra are identical for both descriptions, however the
identification is more subtle.Comment: 32 pages, 2 figure
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