54 research outputs found
A Calogero formulation for four-dimensional black-hole micro states
We extract the leading-order entropy of a four-dimensional extremal black
hole in ungauged supergravity by formulating the CFT that is
holographically dual to its near-horizon AdS geometry, in terms of a
rational Calogero model with a known counting formula for the degeneracy of
states in its Hilbert space.Comment: 8 page
Indefinite theta functions for counting attractor backgrounds
In this note, we employ indefinite theta functions to regularize canonical
partition functions for single-center dyonic BPS black holes. These partition
functions count dyonic degeneracies in the Hilbert space of four-dimensional
toroidally compactified heterotic string theory, graded by electric and
magnetic charges. The regularization is achieved by viewing the weighted sums
of degeneracies as sums over charge excitations in the near-horizon attractor
geometry of an arbitrarily chosen black hole background, and eliminating the
unstable modes. This enables us to rewrite these sums in terms of indefinite
theta functions. Background independence is then implemented by using the
transformation property of indefinite theta functions under elliptic
transformations, while modular transformations are used to make contact with
semi-classical results in supergravity.Comment: 24 pages, LaTe
Comments on the Spectrum of CHL Dyons
We address a number of puzzles relating to the proposed formulae for the
degeneracies of dyons in orbifold compactifications of the heterotic string to
four dimensions with supersymmetry. The partition function for these
dyons is given in terms of Siegel modular forms associated with genus-two
Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance
of the resulting degeneracies and give a prescription that makes the invariance
manifest. We show, using M-theory lift of string webs, that the genus-two
contribution captures the degeneracy only if a specific irreducibility
criterion is satisfied by the charges. Otherwise, in general there can be
additional contributions from higher genus Riemann surfaces. We analyze the
negative discriminant states predicted by the formula. We show that even though
there are no big black holes in supergravity corresponding to these states,
there are multi-centered particle-like configurations with subleading entropy
in agreement with the microscopic prediction and our prescription for S-duality
invariance. The existence of the states is moduli dependent and we exhibit the
curves of marginal stability and comment on its relation to S-duality
invariance.Comment: 23 pages, 3 figure
Spectrum of dyons and black holes in CHL orbifolds using borcherds lift
The degeneracies of supersymmetric quarter BPS dyons in four dimensions and of spinning black holes in five dimensions in a CHL compactification are computed exactly using Borcherds lift. The Hodge anomaly in the construction has a physical interpretation as the contribution of a single M-theory Kaluza-Klein 6-brane in the 4d-5d lift. Using factorization, it is shown that the resulting formula has a natural interpretation as a two-loop partition function of left-moving heterotic string, consistent with the heuristic picture of dyons in the M-theory lift of string webs
Heating up branes in gauged supergravity
In this note, we explore the solution space of non-extremal black objects in
and gauged supergravity in the presence of fluxes. We
present first order rewritings of the action for a classes of non-extremal
dyonic and electric solutions with electric flux backgrounds. Additionally, we
obtain the non-extremal version of the Nernst brane in using a simple
deformation. Finally, we develop a new technique to deform extremal black
solutions in to non-extremal solutions by an analysis of the symmetries of
the equations of motion.Comment: Minor typographic correction
Counting Strings, Wound and Bound
We analyze zero mode counting problems for Dirac operators that find their
origin in string theory backgrounds. A first class of quantum mechanical models
for which we compute the number of ground states arises from a string winding
an isometric direction in a geometry, taking into account its energy due to
tension. Alternatively, the models arise from deforming marginal bound states
of a string winding a circle, and moving in an orthogonal geometry. After
deformation, the number of bound states is again counted by the zero modes of a
Dirac operator. We count these bound states in even dimensional asymptotically
linear dilaton backgrounds as well as in Euclidean Taub-NUT. We show multiple
pole behavior in the fugacities keeping track of a U(1) charge. We also discuss
a second class of counting problems that arises when these backgrounds are
deformed via the application of a heterotic duality transformation. We discuss
applications of our results to Appell-Lerch sums and the counting of domain
wall bound states.Comment: 38 page
Indefinite theta functions and black hole partition functions
We explore various aspects of supersymmetric black hole partition functions
in four-dimensional toroidally compactified heterotic string theory. These
functions suffer from divergences owing to the hyperbolic nature of the charge
lattice in this theory, which prevents them from having well-defined modular
transformation properties. In order to rectify this, we regularize these
functions by converting the divergent series into indefinite theta functions,
thereby obtaining fully regulated single-centered black hole partitions
functions.Comment: 35 pages; v2: various comments added; v3: a few typos correcte
Generalized Hot Attractors
Non-extremal black holes are endowed with geometric invariants related to
their horizon areas. We extend earlier work on hot attractor black holes to
higher dimensions and add a scalar potential. In addition to the event and
Cauchy horizons, when we complexify the radial coordinate, non-extremal black
holes will generically have other horizons as well. We prove that the product
of all of the horizon areas is independent of variations of the asymptotic
moduli further generalizing the attractor mechanism for extremal black holes.
In the presence of a scalar potential, as typically appears in gauged
supergravity, we find that the product of horizon areas is not necessarily the
geometric mean of the extremal area, however. We outline the derivation of
horizon invariants for stationary backgrounds.Comment: 39 pages, 3 figures, v2 references and clarifications adde
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