246 research outputs found
Global anomaly and a family of structures on fold product of complex two-cycles
We propose a new set of IIB type and eleven-dimensional supergravity
solutions which consists of the -fold product of two-spaces (where denotes the product of upper half-planes
equipped with the co-compact action of ) and (where and is a congruence subgroup of ). The
Freed-Witten global anomaly condition have been analyzed. We argue that the
torsion part of the cuspidal cohomology involves in the global anomaly
condition. Infinitisimal deformations of generalized complex (and K\"ahler)
structures also has been analyzed and stability theorem in the case of a
discrete subgroup of with the compact quotient was verified.Comment: 7 pages, no figures. To appear in the Proceedings of XXVIII Workshop
on Geometrical Methods in Physics, Bialowieza (Poland), 28.06 - 04.07.200
BRST-Invariant Deformations of Geometric Structures in Sigma Models
We study a Lie algebra of formal vector fields with its application to
the perturbative deformed holomorphic symplectic structure in the A-model, and
a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent
classes of deformations are describing by a Hochschild cohomology theory of the
DG-algebra , ,
which is defined to be the cohomology of . Here
is the initial non-deformed BRST operator while is the deformed part whose algebra is a Lie algebra of linear vector
fields . We show that equivalent classes of deformations are
described by a Hochschild cohomology of , an important geometric
invariant of the (anti)holomorphic structure on . We discuss the
identification of the harmonic structure
of affine space and the group {\rm Ext}_{X^{2}}^n({\cO}_{\triangle},
{\cO}_{\triangle}) (the HKR isomorphism), and bulk-boundary deformation
pairing.Comment: 13 pages, no figure
Thermodynamics of Abelian Gauge Fields in Real Hyperbolic Spaces
We work with dimensional compact real hyperbolic space with
universal covering and fundamental group . Therefore, is the
symmetric space , where and is a maximal compact
subgroup of . We regard as a discrete subgroup of acting
isometrically on , and we take to be the quotient space by that
action: . The natural
Riemannian structure on (therefore on ) induced by the Killing form of
gives rise to a connection form Laplacian on the quotient
vector bundle (associated with an irreducible representation of K). We study
gauge theories based on abelian forms on the real compact hyperbolic
manifold . The spectral zeta function related to the operator
, considering only the co-exact part of the forms and
corresponding to the physical degrees of freedom, can be represented by the
inverse Mellin transform of the heat kernel. The explicit thermodynamic
fuctions related to skew-symmetric tensor fields are obtained by using the
zeta-function regularization and the trace tensor kernel formula (which
includes the identity and hyperbolic orbital integrals). Thermodynamic
quantities in the high and low temperature expansions are calculated and new
entropy/energy ratios established.Comment: Six pages, Revtex4 style, no figures; small typo correcte
Hyperbolic Topological Invariants and the Black Hole Geometry
We discuss the isometry group structure of three-dimensional black holes and
Chern-Simons invariants. Aspects of the holographic principle relevant to black
hole geometry are analyzed.Comment: 11 pages, AMSTeX, Contribution to the Fifth Alexander Friedmann
International Seminar on Gravitation and Cosmolog
Quantum State Density and Critical Temperature in M-theory
We discuss the asymptotic properties of quantum states density for
fundamental branes which can yield a microscopic interpretation of the
thermodynamic quantities in M-theory. The matching of BPS part of spectrum for
superstring and supermembrane gives the possibility of getting membrane's
results via string calculations. In the weak coupling limit of M-theory the
critical behavior coincides with the first order phase transition in standard
string theory at temperature less than the Hagedorn's temperature . The
critical temperature at large coupling constant is computed by considering
M-theory on manifold with topology .
Alternatively we argue that any finite temperature can be introduced in the
framework of membrane thermodynamics.Comment: 16 pages, published in Mod. Phys. Lett. A16(2001)224
Statistical entropy of near-extremal and fundamental black p-branes
The problem of asymptotic density of quantum states of fundamental extended
objects is revised in detail. We argue that in the near-extremal regime the
fundamental -brane approach can yield a microscopic interpretation of the
black hole entropy. The asymptotic behavior of partition functions, associated
with the -branes, and the near-extremal entropy of five-dimensional black
holes are explicitly calculated.Comment: 15 pages, LateX file.Minor changes,refs added, version to appear in
Progr.Theor.Phy
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