arXiv subjects

Anindya Dey

Publications and source records attributed to Anindya Dey.

28 records · Page 2Linked to original sources

arXiv2014

Hyperkahler Sigma Model and Field Theory on Gibbons-Hawking Spaces

We describe a novel deformation of the 3-dimensional sigma model with hyperkähler target, which arises naturally from the compactification of a 4-dimensional $\mathcal{N}=2$ theory on a hyperkähler circle bundle (Gibbons-Hawking space). We derive the condition for which the deformed sigma model preserves 4 out of the 8 supercharges. We also study the contribution from a NUT center to the sigma model path integral, and find that supersymmetry implies it is a holomorphic section of a certain holomorphic line bundle over the hyperkähler target. We study explicitly the case where the original 4-dimensional theory is pure $U(1)$ super Yang-Mills, and show that the contribution from a NUT center in this case is simply the Jacobi theta function.

hep-th↗

arXiv2013

Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.

hep-th↗

arXiv2013

Three Dimensional Mirror Symmetry and Partition Function on $S^3$

We provide non-trivial checks of $\mathcal{N}=4, D=3$ mirror symmetry in a large class of quiver gauge theories whose Type IIB (Hanany-Witten) descriptions involve D3 branes ending on orbifold/orientifold 5-planes at the boundary. From the M-theory perspective, such theories can be understood in terms of coincident M2 branes sitting at the origin of a product of an A-type and a D-type ALE (Asymtotically Locally Euclidean) space with G-fluxes. Families of mirror dual pairs, which arise in this fashion, can be labeled as $(A_{m-1},D_n)$, where $m$ and $n$ are integers. For a large subset of such infinite families of dual theories, corresponding to generic values of $n\geq 4$, arbitrary ranks of the gauge groups and varying $m$, we test the conjectured duality by proving the precise equality of the $S^3$ partition functions for dual gauge theories in the IR as functions of masses and FI parameters. The mirror map for a given pair of mirror dual theories can be read off at the end of this computation and we explicitly present these for the aforementioned examples. The computation uses non-trivial identities of hyperbolic functions including certain generalizations of Cauchy determinant identity and Schur's Pfaffian identity, which are discussed in the paper.

hep-th↗

arXiv2012

Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II

We continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar momenta gives rise to enhanced non-Gaussianity in certain squeezed triangle configurations, although the enhancement of the $f_{NL}$ parameter is limited by the breakdown of linear perturbation theory at "exact planarity". Finally, we demonstrate that for the range of planar modes for which scale invariance of the power spectrum is preserved, non-Gaussianity in the curvature perturbation spectrum is naturally constrained to be extremely small.

astro-ph.CO↗

arXiv2012

Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy

We investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three-point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon after isotropization. In this momentum regime, the early time dynamics admits a WKB description and the late time dynamics can be described in terms of a non-Bunch Davies vacuum state which encodes the information of initial anisotropy in the background spacetime. We compute the bi-spectrum for curvature perturbation in a canonical single-field action with and without higher derivative operators. We show that the bi-spectrum at late times, in either case, is enhanced for a flattened triangle configuration as well as a squeezed triangle configuration and compute the corresponding $f_{NL}$ parameters. The angular dependence and the particular momentum dependence of the $f_{NL}$ parameter appear as distinctive features of background anisotropy at early times.

hep-th↗

arXiv2012

On Three-Dimensional Mirror Symmetry

Mirror Symmetry for a large class of three dimensional $\mathcal{N}=4$ supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of $\text{ALE}$ spaces. A pair of such mirror duals can be described as two different deformations of the eleven-dimensional supergravity background $\mathcal{M}=\mathbb{R}^{2,1} \times \text{ALE}_{1} \times \text{ALE}_{2}$, to which they flow in the deep IR. Using the $A-D-E$ classification of $\text{ALE}$ spaces, we present a neat way to catalogue dual quiver gauge theories that arise in this fashion. In addition to the well-known examples studied in \cite{Intriligator:1996ex}, \cite{deBoer:1996mp}, this procedure leads to new sets of dual theories. For a certain subset of dual theories which arise from the aforementioned M-theory background with an $A$-type $\text{ALE}_{1}$ and a $D$-type $\text{ALE}_2$, we verify the duality explicitly by a computation of partition functions of the theories on $S^3$, using localization techniques . We derive the relevant mirror map and discuss its agreement with predictions from the Type IIB brane construction for these theories.

hep-th↗

arXiv2008

Stability and hierarchy problems in string inspired braneworld scenarios

We generalise the RS braneworld model by taking into account a general stringy bulk containing the scalar dilaton field and the two-form Kalb-Ramond field, apart from gravity. Assuming small fluctuations around a RS background, the back-reacted warp factor is obtained. It is shown that the fine tuning problem in connection with the Higgs mass reappears in a new guise and the effective modular potential fails to stabilise the braneworld.

hep-th↗

arXiv2006

A Critical Analysis of Goldberger-Wise Stabilization in Randall-Sundrum Scenario

The Goldberger-Wise mechanism of stabilizing modulus in the Randall-Sundrum braneworld,by introducing a bulk scalar field with quartic interaction terms localized at the 3-branes has been extremely popular as a stabilizing mechanism when the back-reaction of the scalar field on the geometry is negligibly small. In this note we re-examine the mechanism by an exact analysis without resorting to the approximations adopted by Goldberger and Wise. An exact calculation of the stabilization condition indicates the existence of closely spaced minimum and a maximum for the potential and also brings out some new features involved in the context of stabilization of such braneworld models.

hep-th↗

arXiv2006

Randall-Sundrum with Kalb-Ramond field: return of the hierarchy problem?

We show that when the antisymmetric Kalb-Ramond field is included in the Randall-Sundrum scenario, although the hierarchy problem can be solved, it requires an extreme fine tuning of the Kalb-Ramond field (about 1 part in $10^{62}$). We interpret this as the return of the problem in disguise. Further, we show that the Kalb-Ramond field induces a small negative cosmological constant on the visible brane.

gr-qc↗

arXiv2006

Readdressing the hierarchy problem in a Randall-Sundrum scenario with bulk Kalb-Ramond background

We re-examine the fine tuning problem of the Higgs mass, when an antisymmetric two form Kalb-Ramond (KR) field is present in the bulk of a Randall-Sundrum (RS) braneworld. Taking into account the back-reaction of the KR field, we obtain the exact correction to the RS metric. The modified metric also warps the Higgs mass from Planck scale (in higher dimension) to TeV scale (on the visible brane) for a range of values of $kr$ exceeding the original RS value (where $k=$ Planck mass and $r=$ size of extra dimension). However, it requires an extraordinary suppression of the KR field density, indicating the re-appearence of the fine tuning problem in a different guise. The new spacetime also generates a small negative cosmological constant on the visible brane. These results are particularly relevant for certain string based models, where the KR field is unavoidably present in the bulk. We further show that such a bulk antisymmetric KR field fails to stabilize the braneworld.

hep-th↗