arXiv subjects

Bhupendra Nath Tiwari

Publications and source records attributed to Bhupendra Nath Tiwari.

27 records · Page 2Linked to original sources

arXiv2010

A geometric approach to correlations and quark number susceptibilities

We study the thermodynamic geometry arising from the free energy for the 2- and 3-flavor finite temperature hot QCD near the critical temperature. We develop a geometric notion for QCD thermodynamics, relating it with the existing microscopic quantities, e.g. quark-number susceptibility, which appears naturally within an approximately self-consistent resummation of perturbative QCD. We further incorporate thermal fluctuations in the free energy, thus yielding the geometric properties of local and global chemical correlations. These investigations are perturbative in nature. Nevertheless, one could apply the same line of thought for the geometric realization of underlying quark susceptibilities, either in the fabric of lattice QCD or in that of non-perturbative QCD.

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arXiv2010

Thermodynamic Geometric Stability of Quarkonia states

We compute exact thermodynamic geometric properties of the non-abelian quarkonium bound states from the consideration of one-loop strong coupling. From the general statistical principle, the intrinsic geometric nature of strongly coupled QCD is analyzed for the Columbic, rising and Regge rotating regimes. Without any approximation, we have obtained the non-linear mass effect for the Bloch-Nordsieck rotating strongly coupled quarkonia. For a range of physical parameters, we show in each cases that there exists a well-defined, non-degenerate, curved, intrinsic Riemannian manifold. As the gluons become softer and softer, we find in the limit of the Bloch-Nordsieck resummation that the strong coupling obtained from the Sudhakov form factor possesses exact local and global thermodynamic properties of the underlying mesons, kaons and $D_s$ particles.

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arXiv2010

Black Strings, Black Rings and State-space Manifold

State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and $M$-theory. We have explicitly examined the case of unit Kaluza-Klein momentum $D_1D_5P$ black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, {\it viz.}, the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating $D_1D_5$ black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued $M_5$-dipole charged rotating circular strings and Maldacena Strominger Witten black rings exhibit non-degenerate, positively curved, comprehensively regular state-space configurations. Furthermore, the state-space geometry of single bubbled rings admits a well-defined, positive definite, everywhere regular and curved intrinsic Riemannian manifold; except for the two finite values of conserved electric charge. We also discuss the implication and potential significance of this work for the physics of black holes in string theory.

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arXiv2010

On the Thermodynamic Geometry of Hot QCD

We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of 2- and 3-flavor hot QCD with or without including thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities in hot QCD.

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arXiv2010

An Exact Fluctuating 1/2-BPS Configuration

This work explores the role of thermodynamic fluctuations in the two parameter giant and superstar configurations characterized by an ensemble of arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis illustrates that the chemical and state-space geometric descriptions exhibit an intriguing set of exact pair correction functions and the global correlation lengths. The first principle of statistical mechanics shows that the possible canonical fluctuations may precisely be ascertained without any approximation. Interestingly, our intrinsic geometric study exemplifies that there exist exact fluctuating 1/2-BPS statistical configurations which involve an ensemble of microstates describing the liquid droplets or fuzzballs. The Gaussian fluctuations over an equilibrium chemical and state-space configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds for all physically admissible domains of black hole parameters. An explicit computation demonstrates that the underlying chemical correlations involve ordinary summations, whilst the state-space correlations may simply be depicted by standard polygamma functions. Our construction ascribes definite stability character to the canonical energy fluctuations and to the counting entropy associated with an arbitrary choice of excited boxes from an ensemble of ample boxes constituting a variety of Young tableaux.

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arXiv2009

State-space Correlations and Stabilities

The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the $D_6$-$D_4$-$D_2$-$D_0$ multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present consideration. In the case of extremal black brane configurations, we have pointed out that the ratio of diagonal space-state correlations varies as inverse square of the chosen parameters, while the off diagonal components vary as inverse of the chosen parameters. We discuss the significance of this observation for the non-extremal black brane configurations, and find similar conclusion that the state-space correlations extenuate as the chosen parameters are increased.

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arXiv2008

On the Microscopic Perspective of Black Branes Thermodynamic Geometry

In this article we study correspondence between the microscopic spectrum and macroscopic properties of a class of extremal and non-extremal black branes and outline an origin of the interactions among various microstates of a given black brane configuration from the perspective of an intrinsic Riemannian geometry arising from the coarse graining entropy over a large number of microstates. We have analyzed the state-space geometry in the case of various extremal and non-extremal black branes arising from the string theories, multi-centered black brane configurations, small black holes with fractional branes, fuzzy rings in the set up of Mathur's fuzzballs and subensemble theory, as well as that the black brane foams from the considerations of bubbling black brane solutions in the M-theory. We have further shown that there exists a clear mechanism on the black brane side that describes the notion of associated interactions in the state-space or vice-versa. We thus find that in all such cases there are no singularities in the state-space manifold of these black brane configurations. This observation is in turn consistent with the existing picture of corresponding microscopic CFT data.

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arXiv2008

Thermodynamic Geometry and Extremal Black Holes in String Theory

We study a generalisation of thermodynamic geometry to degenerate quantum ground states at zero temperatures exemplified by charged extremal black holes in type II string theories. Several examples of extremal charged black holes with non degenerate thermodynamic geometries and finite but non zero state space scalar curvatures are established. These include black holes described by D1-D5-P and D2-D6-NS5-P brane systems and also two charged small black holes in Type II string theories. We also explore the modifications to the state space geometry and the scalar curvature due to the higher derivative contributions and string loop corrections as well as an exact entropy expression from quantum information theory. Our construction describes state space geometries arising out of a possible limiting thermodynamic characterisation of degenerate quantum ground states at zero temperatures.

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arXiv2006

On the Thermodynamic Geometry of BTZ Black Holes

We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.

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