arXiv subjects

Raju Roychowdhury

Publications and source records attributed to Raju Roychowdhury.

At least 19 recordsLinked to original sources

arXiv2026

Towards a T-dual Emergent Gravity

Emergent gravity provides a geometric realization of noncommutative U(1) gauge theory, in which gauge-field deformations of a symplectic structure are absorbed by diffeomorphisms through the Darboux theorem, giving rise to an effective Riemannian metric. Independently, topological T-duality relates principal torus bundles with different geometric and flux data whose associated sigma models are physically equivalent. We unify these two constructions within the framework of generalized geometry by formulating emergent gravity in terms of generalized metrics on exact Courant algebroids. In this description, the Seiberg-Witten map is naturally interpreted as a composition of B-transformations and theta-transformations acting on a flat background. Using the Gualtieri-Cavalcanti isomorphism of Courant algebroids, we construct a notion of T-dual emergent gravity for principal torus bundles and derive the corresponding dual generalized metrics. For flat backgrounds with vanishing H-flux, we show that the T-dual generalized metric again admits an emergent gravity interpretation, encoded by a commutative diagram in which T-duality exchanges the order of the transformations generating the emergent metric. For general two-torus fibrations, we obtain explicit expressions for the dual generalized metric and demonstrate that the dual background generically carries nontrivial H-flux, obstructing a conventional symplectic formulation of emergent gravity and motivating an extension to non-exact Courant algebroids. These results establish a precise mathematical correspondence between emergent gravity and topological T-duality, and identify generalized geometry as the natural framework for a T-duality-covariant formulation of emergent gravity in both geometric and flux backgrounds.

hep-th↗

arXiv2025

A Mathematical Model to Capture Urbanization Trajectory Induced by Economic Inequality

Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating growth, (ii) continuously decelerating growth, (iii) two-phase growth transitioning from acceleration to deceleration, and (iv) two-phase growth transitioning from deceleration to acceleration. To understand the origin of these diverse urbanization trajectories, we develop a simple coarse-grained model in which a country is segregated into two regions, a rural and an urban region. Population in each region evolves due to natural (sexual) growth and migration from rural to urban areas, with the migration rate governed by economic inequality, quantified through the difference in GDP per capita between the two regions. The GDP per capita of both regions is assumed to grow exponentially with distinct rates. We demonstrate that this minimal model, involving four dynamical variables and a small number of demographic and economic parameters, is capable of reproducing all four empirically observed urbanization patterns. Assuming demographic and economic parameters remain approximately constant over a 50-year timescale, we estimate coarse-grained parameters for the United States using empirical data and obtain optimized values that accurately reproduce its observed urbanization trajectory. Our results highlight how simple demographic-economic interactions can generate rich and diverse urbanization dynamics.

physics.soc-ph↗

arXiv2023

T-duality of emergent gravities on nilmanifolds

We study the transport of generalized metrics between topological T-dual nilmanifolds through a Lie algebraic point of view. Emergent gravities are generalized metrics with symplectic B-fields. But this additional property might not be preserved by the aforementioned transport. We describe a necessary condition for it to happen and provide working examples on self-T-dual nilmanifolds with zero $H$-flux in both 4 and 6 dimensions. We also discuss how this procedure fails in the presence of a non-zero $H$-flux.

hep-th↗

arXiv2018

Manifold Ways to Darboux-Halphen System

Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of double orthogonal surfaces in $\mathbb{R}^3$. The second is a problem in general relativity about gravitational instanton in Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called Gauss-Manin connection in disguise developed by one of the authors and finally in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold.

math.DG↗

arXiv2016

Schwarzschild Instanton in Emergent Gravity

In the bottom-up approach of emergent gravity we attempt to find symplectic gauge fields emerging from Euclidean Schwarzschild instanton, which is studied as electromagnetism defined on the symplectic space $(M,ω)$. Geometrical engineering with the emergent metric sets up the Seiberg Witten map between commutative and non-commutative gauge fields, preparing the ground for the evaluation of topological invariants in terms of the underlying gauge theory quantities.

hep-th↗

arXiv2016

Taub-NUT as Bertrand spacetime with magnetic fields

Based on symmetries Taub-NUT shares with Bertrand spacetime, we cast it as the latter with magnetic fields. Its nature as a Bianchi-IX gravitational instanton and other related geometrical properties are reviewed. We provide an easy derivation and comparison between the spatial Killing-Yano tensors deduced from first-integrals and the corresponding hyperkähler structures and finally verify the existence of a graded Lie-algebra structure via Schouten-Nijenhuis brackets.

hep-th↗

arXiv2016

Anti Self-Dual Yang-Mills, Modified Faddeev-Jackiw Formalism and Hidden BRS Invariance

We analyze the constraints for a system of anti self-dual Yang-Mills (ASDYM) equations by means of the modified Faddeev-Jackiw method in K and J gauges à la Yang. We also establish the Hamiltonian flow for ASDYM system through the hidden BRS invariance in both the gauges. Finally, we remark on the bi-Hamiltonian nature of ASDYM and the compatibility of the symplectic structures therein.

hep-th↗

arXiv2016

From pseudo-holomorphic functions to the associated real manifold

This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the differential inequalities describing pseudo-holomorphic functions can be used to define a one-real-dimensional manifold (by the vanishing of a function with nonzero gradient), which is here a 1-parameter family of plane curves. On studying the associated envelopes, such a parameter can be eliminated by solving two nonlinear partial differential equations. The classical differential geometry of curves can be therefore exploited to get a novel perspective on the equations describing the global theory of pseudo-holomorphic functions.

math.CV↗

arXiv2016

First integrals of Generalized Darboux-Halphen systems and Membrane Paradigm

The Darboux-Halphen system of equations have common or individual additive terms depending on the matrices defining Yang-Mills gauge potential fields. Tod (Phys. Lett. A 190 (1994) 221-224), described a conserved quantity for the classical systems with no additive terms. We show that the conserved quantity apply even for the generalized cases with common additive terms. A theory has been presented, with an example, of how to formulate conserved quantities for equation with individual additive terms. We also briefly shed some light on the issues of surface motions of fluids in conncetion to Nahm`s equation and the self-duality and integrability of membrane dynamics.

hep-th↗

arXiv2016

Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan

Bianchi-IX four metrics are $SU(2)$ invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler Top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux-Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux-Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang-Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux-Halphen system and occurring in the study of Bianchi IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.

hep-th↗

arXiv2013

Test of Emergent Gravity

In this paper we examine a small but detailed test of the emergent gravity picture with explicit solutions in gravity and gauge theory. We first derive symplectic U(1) gauge fields starting from the Eguchi-Hanson metric in four-dimensional Euclidean gravity. The result precisely reproduces the U(1) gauge fields of the Nekrasov-Schwarz instanton previously derived from the top-down approach. In order to clarify the role of noncommutative spacetime, we take the Braden-Nekrasov U(1) instanton defined in ordinary commutative spacetime and derive a corresponding gravitational metric. We show that the Kähler manifold determined by the Braden-Nekrasov instanton exhibits a spacetime singularity while the Nekrasov-Schwarz instanton gives rise to a regular geometry-the Eguchi-Hanson space. This result implies that the noncommutativity of spacetime plays an important role for the resolution of spacetime singularities in general relativity. We also discuss how the topological invariants associated with noncommutative U(1) instantons are related to those of emergent four-dimensional Riemannian manifolds according to the emergent gravity picture.

hep-th↗

arXiv2013

Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity

Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a spacetime with symplectic structure. In this approach, the spacetime geometry is defined by U(1) gauge fields on noncommutative (NC) spacetime. Accordingly the topology of spacetime is determined by the topology of NC U(1) gauge fields. We show that the topology change of spacetime is ample in emergent gravity and the subsequent resolution of spacetime singularity is possible in NC spacetime. Therefore the emergent gravity approach provides a well-defined mechanism for the topology change of spacetime which does not suffer any spacetime singularity in sharp contrast to general relativity.

hep-th↗

arXiv2013

Transport in non-conformal holographic fluids

We have considered non-conformal fluid dynamics whose gravity dual is a certain Einstein dilaton system with Liouville type dilaton potential, characterized by an intrinsic parameter $η$. We have discussed the Hawking-Page transition in this framework using hard-wall model and it turns out that the critical temperature of the Hawking-Page transition encapsulates a non-trivial dependence on $η$. We also obtained transport coefficients such as AC conductivity, shear viscosity and diffusion constant in the hydrodynamic limit, which show non-trivial $η$ dependent deviations from those in conformal fluids, although the ratio of the shear viscosity to entropy density is found to saturate the universal bound. Some of the retarded correlators are also computed in the high frequency limit for case study.

hep-th↗

arXiv2012

Non-conformal Hydrodynamics in Einstein-dilaton Theory

In the Einestein-dilaton theory with a Liouville potential parameterized by $η$, we find a Schwarzschild-type black hole solution. This black hole solution, whose asymptotic geometry is described by the warped metric, is thermodynamically stable only for $0 \le η< 2$. Applying the gauge/gravity duality, we find that the dual gauge theory represents a non-conformal thermal system with the equation of state depending on $η$. After turning on the bulk vector fluctuations with and without a dilaton coupling, we calculate the charge diffusion constant, which indicates that the life time of the quasi normal mode decreases with $η$. Interestingly, the vector fluctuation with the dilaton coupling shows that the DC conductivity increases with temperature, a feature commonly found in electrolytes.

hep-th↗

arXiv2012

Notes on Emergent Gravity

Emergent gravity is aimed at constructing a Riemannian geometry from U(1) gauge fields on a noncommutative spacetime. But this construction can be inverted to find corresponding U(1) gauge fields on a (generalized) Poisson manifold given a Riemannian metric (M, g). We examine this bottom-up approach with the LeBrun metric which is the most general scalar-flat Kahler metric with a U(1) isometry and contains the Gibbons-Hawking metric, the real heaven as well as the multi-blown up Burns metric which is a scalar-flat Kahler metric on C^2 with n points blown up. The bottom-up approach clarifies some important issues in emergent gravity.

hep-th↗

arXiv2011

On the transition from complex to real scalar fields in modern cosmology

We study some problems arising from the introduction of a complex scalar field in cosmology, modelling its possible behaviors in both the inflationary and dark energy stages of the universe. Such examples contribute to show that, while the complex nature of the scalar field can be indeed important during inflation, it loses its meaning in the later dark-energy dominated era of cosmology, when the phase of the complex field is practically constant, and there is indeed a transition from complex to real scalar field. In our considerations, the Noether symmetry approach turns out to be a useful tool once again. We arrive eventually at a potential containing the sixth and fourth powers of the scalar field, and the resulting semiclassical quantum cosmology is studied to gain a better understanding of the inflationary stage.

hep-th↗

arXiv2010

A Study on Charged Neutron Star in $AdS_5$

Motivated by an open question raised in recent times regarding the phase transition during the collapse of a neutron star to form a black hole and related stability issues, we have constructed charged neutron stars in $AdS_5$ and show that these stars become unstable at a particular value of their radius, regarded as the Chandrasekhar radius. We reproduced the calculations recently done in [20] in our $AdS_5$ charged star. The analysis shows that the non-Fermi liquid behavior found there in $AdS_4$ is still true in this higher dimensional case with the presence of Kosevich-Lifshitz oscillations.

hep-th↗

arXiv2010

Topics in Cubic Special Geometry

We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbits, which we classify in some detail within the "special coordinates" symplectic frame. Finally, after a brief account of the action of PQ transformations on the recently established correspondence between Cayley's hyperdeterminant and elliptic curves, we derive an equivalent, alternative expression of I4, with relevant application to black hole entropy.

hep-th↗