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Sachindeo Vaidya

Publications and source records attributed to Sachindeo Vaidya.

34 records · Page 2Linked to original sources
arXiv2013

Monopoles On $S^2_F$ From The Fuzzy Conifold

The intersection of the conifold $z_1^2+z_2^2+z_3^2 =0$ and $S^5$ is a compact 3--dimensional manifold $X^3$. We review the description of $X^3$ as a principal U(1) bundle over $S^2$ and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza--Klein reduction of $X^3$ to $S^2$ provides an easy construction of these monopoles. Using the analogue of the Jordon-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration $X^3 \rightarrow S^2$ and the associated line bundles. This is an alternative new realization of the fuzzy sphere $S^2_F$ and monopoles on it.

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arXiv2013

Renormalization of Noncommutative Quantum Field Theories

We report on a comprehensive analysis of the renormalization of noncommutative ϕ^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincaré invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and β-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative LSZ formalism.

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arXiv2012

Non-Extremality, Chemical Potential and the Infrared limit of Large N Thermal QCD

Non-extremal solution with warped resolved-deformed conifold background is important to study the infrared limit of large N thermal QCD. Earlier works in this direction have not taken into account all the back-reactions on the geometry, namely from the branes, fluxes, and black-hole carefully. In the present work we make some progress in this direction by solving explicitly the supergravity equations of motions in the presence of the backreaction from the black-hole. The backreactions from the branes and the fluxes on the other hand and to the order that we study, are comparatively suppressed. Our analysis reveal, among other things, how the resolution parameter would depend on the horizon radius and how the RG flows of the coupling constants should be understood in these scenarios, including their effects on the background three-form fluxes. We also study the effect of switching on a chemical potential in the background and, in a particularly simplified scenario, compute the actual value of the chemical potential for our case.

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arXiv2011

Noncommutative Vortices and Instantons from Generalized Bose Operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

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arXiv2010

Uniformly Accelerated Observer in Moyal Spacetime

In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum of the inertial observer appears thermal to the accelerated observer, also known as the Unruh effect. We argue that an accelerating frame may be similarly defined (i.e. as a sequence of instantaneous Lorentz transformations) in noncommutative Moyal spacetime, and discuss the twisted quantum field theory appropriate for such an accelerated observer. Our analysis shows that there are several new features in the case of noncommutative spacetime: chiral massless fields in $(1+1)$ dimensions have a qualitatively different behavior compared to massive fields. In addition, the vacuum of the inertial observer is no longer an equilibrium thermal state of the accelerating observer, and the Bose-Einstein distribution acquires $θ$-dependent corrections.

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arXiv2010

Fate of the Superconducting Ground State on the Moyal Plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is {\it smaller} compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt.

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arXiv2010

Thermal Correlation Functions of Twisted Quantum Fields

We derive the thermal correlators for twisted quantum fields on noncommutative spacetime. We show that the thermal expectation value of the number operator is same as in commutative spacetime, but that higher correlators are sensitive to the noncommutativity parameters $θ^{μν}$.

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arXiv2007

The quantum sinh-Gordon model in noncommutative (1+1) dimensions

Using twisted commutation relations we show that the quantum sinh-Gordon model on noncommutative space is integrable, and compute the exact two-particle scattering matrix. The model possesses a strong-weak duality, just like its commutative counterpart.

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arXiv2004

Quantum Topology Change and Large N Gauge Theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection $X$ of $N$ one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator $D$. The set of boundary conditions encodes the topology and is parameterized by unitary matrices $g_N$. A particular geometry is described by a spectral triple $x(g_N)=(A_X,{\cal H}_X, D(g_N))$. We define a partition function for the sum over all $g_N$. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. In the simplest case the model has one free-parameter $β$ and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at $β=\infty$ for any value of $N$. Moreover, the system undergoes a third-order phase transition at $β=1$ for large $N$. We give a topological interpretation of the phase transition by looking how it affects the topology.

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arXiv2003

On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry

Scalar field theories with quartic interaction are quantized on fuzzy $S^2$ and fuzzy $S^2\times S^2$ to obtain the 2- and 4-point correlation functions at one-loop. Different continuum limits of these noncommutative matrix spheres are then taken to recover the quantum noncommutative field theories on the noncommutative planes ${\mathbb R}^2$ and ${\mathbb R}^4$ respectively. The canonical limit of large stereographic projection leads to the usual theory on the noncommutative plane with the well-known singular UV-IR mixing. A new planar limit of the fuzzy sphere is defined in which the noncommutativity parameter $θ$, beside acting as a short distance cut-off, acts also as a conventional cut-off $Λ=\frac{2}θ$ in the momentum space. This noncommutative theory is characterized by absence of UV-IR mixing. The new scaling is implemented through the use of an intermediate scale that demarcates the boundary between commutative and noncommutative regimes of the scalar theory. We also comment on the continuum limit of the $4-$point function.

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arXiv2001

Scalar Multi-Solitons on the Fuzzy Sphere

We study solitons in scalar theories with polynomial interactions on the fuzzy sphere. Such solitons are described by projection operators of rank k, and hence the moduli space for the solitons is the Grassmannian Gr(k,2j+1). The gradient term of the action provides a non-trivial potential on Gr(k,2j+1), thus reducing the moduli space. We construct configurations corresponding to well-separated solitons, and show that although the solitons attract each other, the attraction vanishes in the limit of large j. In this limit, it is argued that the moduli space is CP^k. For the k-soliton bound state, the moduli space is simply CP^1, all other moduli being lifted. We find that the moduli space of multi-solitons is smooth and that there are no singularities as several solitons coalesce. When the fuzzy S^2 is flattened to a noncommutative plane, we find agreement with the known results, modulo some operator-ordering ambiguities. This suggests that the fuzzy sphere is a natural way to regulate the noncommutative plane both in the ultraviolet and infrared.

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arXiv2001

Perturbative dynamics on fuzzy S^2 and RP^2

By considering scalar theories on the fuzzy sphere as matrix models, we construct a renormalization scheme and calculate the one-loop effective action. Because of UV-IR mixing, the two- and the four-point correlators at low energy are not slowly varying functions of external momenta. Interestingly, we also find that field theories on fuzzy RP^2 avoid UV-IR mixing and hence are much more like conventional field theories. We calculate the one-loop beta-function for the O(N) theory on fuzzy RP^2 at large N and show that in addition to the trivial one, it has a nontrivial fixed point that is accessible in perturbation theory.

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arXiv2000

Fuzzy Cosets and their Gravity Duals

Dp-branes placed in a certain external RR (p+4)-form field expand into a transverse fuzzy two-sphere, as shown by Myers. We find that by changing the (p+4)-form background other fuzzy cosets can be obtained. Three new examples, S^2 X S^2, CP^2 and SU(3)/(U(1) X U(1)) are constructed. The first two are four-dimensional while the last is six-dimensional. The dipole and quadrupole moments which result in these configurations are discussed. Finally, the gravity backgrounds dual to these vacua are examined in a leading order approximation. These are multi-centered solutions containing (p+4)- or (p+6)-dimensional brane singularities.

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arXiv1999

Point Mass Geometries, Spectral Flow and AdS_3-CFT_2 Correspondence

We discuss, in terms of the AdS_3-CFT_2 correspondence, a one-parameter family of (asymptotically AdS_3) conical geometries which are generated by point masses and interpolate between AdS_3 and BTZ spacetimes. We show that these correspond to spectral flow in N= (4,4) SCFT_2 which interpolate between NS and R sectors. Our method involves representing the conical spaces as solutions of three-dimensional supergravity based on the supergroup SU(1,1|2) \times SU(1,1|2). The boundary CFT we use is based on the D1/D5 system. The correspondence includes comparing the Euclidean free energies between supergravity and SCFT for the family of conical spaces including BTZ black holes.

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arXiv1998

Global Anomalies in Canonical Gravity

In this note we study the structure of diffeomorphism anomalies in 3+1 canonical gravity coupled to a chiral massless fermion. We find that when the spatial manifold is S^3 or a Lens space L(p,q), the first homotopy group of the related diffeomorphism group can be nontrivial and hence the question of global anomalies becomes relevant. Here we show that for gravity coupled to SU(2) chiral fermions, assuming the strong form of the Hatcher conjecture, SU(2)-induced diffeomorphism anomalies do not occur whenever the spatial manifold is S^3 or a Lens space.

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