Raju Roychowdhury

Topics in cubic special geometry

We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kahler 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 and 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” char...

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, modeling 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.

Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan

Bianchi-IX four metrics are

ATTRACTOR FLOWS IN st2 BLACK HOLES

SU(2)

On the complete analytic structure of the massive gravitino propagator in four-dimensional de Sitter space

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.

Spinor Two-Point Functions and Peierls Bracket in de Sitter Space

Following the same treatment of Bellucci et al. we obtain, the hitherto unknown general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing and vanishing central charge Z for the so-called st2 model, the minimal rank-two symmetric supergravity in d = 4 space-time dimensions. We also make useful comparisons with results that already exist in literature, and introduce the fake supergravity (first-order) formalism to be used in our analysis. An analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane charge configurations has also been presented.

THE EASTWOOD–SINGER GAUGE IN EINSTEIN SPACES

With the help of the general theory of the Heun equation, this paper completes previous work by the authors and other groups on the explicit representation of the massive gravitino propagator in four-dimensional de Sitter space. As a result of our original contribution, all weight functions which multiply the geometric invariants in the gravitino propagator are expressed through Heun functions, and the resulting plots are displayed and discussed after resorting to a suitable truncation in the series expansion of the Heun function. It turns out that there exist two ranges of values of the independent variable in which the weight functions can be divided into dominant and sub-dominant families.

Schwarzschild instanton in emergent gravity

This paper studies spinor two-point functions for spin-1/2 and spin-3/2 fields in maximally symmetric spaces such as de Sitter (dS) space–time, by using intrinsic geometric objects. The Feynman, positive- and negative-frequency Green functions are then obtained for these cases, from which we eventually display the supercommutator and the Peierls bracket under such a setting in two-component-spinor language.

Antiself-dual Yang–Mills, modified Faddeevs–Jackiw formalism and hidden BRS invariance

Electrodynamics in curved space-time can be studied in the Eastwood–Singer gauge, which has the advantage of respecting the invariance under conformal rescalings of the Maxwell equations. Such a construction is here studied in Einstein spaces, for which the Ricci tensor is proportional to the metric. The classical field equations for the potential are then equivalent to first solving a scalar wave equation with cosmological constant, and then solving a vector wave equation where the inhomogeneous term is obtained from the gradient of the solution of the scalar wave equation. The Eastwood–Singer condition leads to a field equation on the potential which is preserved under gauge transformations provided that the scalar function therein obeys a fourth-order equation where the highest-order term is the wave operator composed with itself. The second-order scalar equation is here solved in de Sitter space-time, and also the fourth-order equation in a particular case, and these solutions are found to admit an exponential decay at large time provided that square-integrability for positive time is required. Last, the vector wave equation in the Eastwood–Singer gauge is solved explicitly when the potential is taken to depend only on the time variable.

On Quantum Special Kaehler Geometry

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.