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M. C. B. Abdalla

Publications and source records attributed to M. C. B. Abdalla.

At least 37 records · Page 2Linked to original sources
arXiv2005

Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds

There is a remarkable connection between the number of quantum states of conformal theories and the sequence of dimensions of Lie algebras. In this paper, we explore this connection by computing the asymptotic expansion of the elliptic genus and the microscopic entropy of black holes associated with (supersymmetric) sigma models. The new features of these results are the appearance of correct prefactors in the state density expansion and in the coefficient of the logarithmic correction to the entropy.

hep-th↗
arXiv2005

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss the modified gravity which includes negative and positive powers of the curvature and which provides the gravitational dark energy. It is shown that in GR plus the term containing negative power of the curvature the cosmic speed-up may be achieved, while the effective phantom phase (with $w$ less than -1) follows when such term contains the fractional positive power of the curvature. The minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fliud may describe the (effective phantom) dark energy. The account of $R^2$ term (consistent modified gravity) may help to escape of cosmic doomsday.

hep-th↗
arXiv2004

General Unitary TFD Formulation for Superstrings

A generalization of the Thermo Field Dynamics (TFD) for fermionic degrees of freedom is proposed. Such a generalization follows a previous one where the SU(1,1) thermal group was used to obtain the closed bosonic string at finite temperature. The SU(2) thermal group is introduced to construct a general thermal Bogoliubov transformation to get the type IIB superstring at finite temperature.

hep-th↗
arXiv2004

Perspectives of TFD on String Theory

Considering the type IIB superstring in a pp wave background some recent ideas and perspectives of Thermo Field Dynamics on string theory are presented. The thermal Fock space is constructed attempting to consider a possible finite temperature version of the BMN correspondence in this framework. Also, the thermal vacuum is identified as a string boundary state realizing the thermal torus interpretation in the ambit of Thermo Field Dynamics. Such a interpretation consists of a generalization of some recent analysis for the closed bosonic string.

hep-th↗
arXiv2004

Formation of Wakes by Chiral, Conducting Cosmic Strings

Chiral cosmic strings are naturally produced at the end of D-term inflation and they present very interesting cosmological consequences. In this work, we investigate the formation and evolution of wakes by a chiral string. We show that, for cold dark matter, the mechanism of forming wakes by a chiral string is similar to the mechanism by an ordinary string.

gr-qc↗
arXiv2004

Superstring in a pp-wave background at finite temperature - TFD approach

A thermodynamical analysis for the type IIB superstring in a pp-wave background is considered. The thermal Fock space is built and the temperature SUSY breaking appears naturally by analyzing the thermal vacuum. All the thermodynamical quantities are derived by evaluating matrix elements of operators in the thermal Fock space. This approach seems to be suitable to study thermal effects in the BMN correspondence context.

hep-th↗
arXiv2003

General Unitary SU(1,1) TFD Formulation

In this work we discuss a generalization for the thermal Bogoliubov transformation in the context of a hermitian general SU(1,1) transformation generator. The TFD tilde conjugation rules are redefined using an appropriated Tomita-Takesaki modular operator.

hep-th↗
arXiv2003

Quantum States, Thermodynamic Limits and Entropy in M-Theory

We discuss the matching of the BPS part of the spectrum for (super)membrane, which gives the possibility of getting membrane's results via string calculations. In the small coupling limit of M--theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at large coupling constant is computed by considering M--theory on a manifold with topology ${\mathbb T}^2\times{\mathbb R}^9$. We argue that the finite temperature partition functions (brane Laurent series for $p \neq 1$) associated with BPS $p-$brane spectrum can be analytically continued to well--defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit $p \to 0$ (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.

hep-th↗
arXiv2003

D-Branes at Finite Temperature in TFD

We review the construction of the $D$-branes at finite temperature as boundary states in the Fock space of thermal perturbative closed string. This is a talk presented by I. V. V. at Common Trends in Cosmology and Particle Physics June 2003, Balatonfured, Hungary.

hep-th↗
arXiv2003

Black Hole Entropy Associated with Supersymmetric Sigma Model

By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ is the symmetric group of $N$ elements) to the partition function of a second quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.

hep-th↗
arXiv2003

TFD Approach to Bosonic Strings and $D_{P}$-branes

In this work we explain the construction of the thermal vacuum for the bosonic string, as well that of the thermal boundary state interpreted as a $D_{p}$-brane at finite temperature. In both case we calculate the respective entropy using the entropy operator of the Thermo Field Dynamics Theory. We show that the contribution of the thermal string entropy is explicitly present in the $D_{p}$-brane entropy. Furthermore, we show that the Thermo Field approach is suitable to introduce temperature in boundary states.

hep-th↗
arXiv2003

Quantum State Density and Critical Temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental $p-$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 $T_H$. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology ${\mathbb R}^9\otimes{mathbb T}^2$. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

hep-th↗
arXiv2002

On The Symplectic Two-Form of Gravity in Terms of Dirac Eigenvalues

The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.

gr-qc↗
arXiv2002

On the SU(1,1) Thermal Group of Bosonic Strings and D-Branes

All possible Bogoliubov operators that generate the thermal transformations in the Thermo Field Dynamics (TFD) form a SU(1,1) group. We discuss this contruction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1,1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are computed. Also, we construct the thermal $D$-brane solution generated by the SU(1,1) transformation in a constant Kalb-Ramond field and compute its entropy.

hep-th↗
arXiv2002

Entropy of Bosonic Open String and Boundary Conditions

The entropy of the states associated to the solutions of the equations of motion of the bosonic open string with combinations of Neumann and Dirichlet boundary conditions is given. Also, the entropy of the string in the states $| A^i > = α^{i}_{-1} |0>$ and $| ϕ^a > = α^{a}_{-1} |0>$ that describe the massless fields on the world-volume of the Dp-brane is computed.

hep-th↗
arXiv2001

Bosonic D-branes at finite temperature with an external field

Bosonic boundary states at finite temperature are constructed as solutions of boundary conditions at $T\neq 0$ for bosonic open strings with a constant gauge field $F_{ab}$ coupled to the boundary. The construction is done in the framework of thermo field dynamics where a thermal Bogoliubov transformation maps states and operators to finite temperature. Boundary states are given in terms of states from the direct product space between the Fock space of the closed string and another identical copy of it. By analogy with zero temperature, the boundary states heve the interpretation of $Dp$-brane at finite temperature. The boundary conditions admit two different solutions. The entropy of the closed string in a $Dp$-brane state is computed and analysed. It is interpreted as the entropy of the $Dp$-brane at finite temperature.

hep-th↗
arXiv2000

Duality between coordinates and Dirac field

The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order.

hep-th↗