arXiv subjects

Zodinmawia

Publications and source records attributed to Zodinmawia.

14 recordsLinked to original sources

arXiv2023

Tidal love number and its influence on the pericenter shift of S-stars near Sgr A*

The tidal love number determines a star's deformability rate in the presence of gravitational potential and depends on the star's internal structure. In this work, we investigate two significant prospects on tidal love number : (i) the influence of the polytropic index of stars on the tidal love number and , (ii) how tidal love number affects the pericenter shift of S-stars near Sgr A* which is an important probe for strong-field tests of gravitational theories. We consider S-stars orbiting Sgr A* at a pericenter distance of 45 au to 500 au, well below the S-2 orbit. The S-stars have polytropic indices of the range, n = 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5, and eccentricity, e = 0.9 inclined at $i=90 ^{\circ}$. The tidal love number is estimated for multipole moments $l=2$ and $l=3$. It has been found that the tidal love number decreases as the polytropic index increases. Additionally, the tidal love number for the multipole moment of $l=2$ is dominant over that of $l=3$. The tidal distortion effect also causes a greater pericenter shift in compact orbit S-stars with lower polytropic indices and tidal love number having multipole moment $l=2$. The estimated results offer relevant insights for testing general relativity and its alternative theories in the vicinity of Sgr A*

astro-ph.GA↗

arXiv2020

BMS Modular Diaries: Torus one-point function

Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.

hep-th↗

arXiv2019

BMS Characters and Modular Invariance

We construct the characters for the highest weight representations of the 3d Bondi-Metzner-Sachs (BMS$_3$) algebra. We then use these to construct the partition function and show how to use BMS modular transformations to obtain a density of primary states. The entropy thus obtained accounts for the principle part of the entropy obtained from the BMS-Cardy formula. This suggests that BMS primaries capture most of the entropy of Flat Space Cosmologies, which are the flatspace analogues of BTZ black holes in AdS$_3$. We reproduce our character formula by looking at singular limits from 2d CFT characters and find that our answers are identical to the characters obtained for the very different induced representations. We offer an algebraic explanation to this arising from a (to the best of our knowledge) novel automorphism in the parent 2d CFT.

hep-th↗

arXiv2018

Supersymmetric Galilean conformal blocks

We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC) field theories in two dimensions by constructing the SGC blocks in the $\mathcal{N}=1$ and two possible $\mathcal{N} =2$ extensions of the Galilean conformal algebra. In all analyzed cases, we present the bootstrap equations by crossing symmetry of the four point function. In addition, we compute the global SGC blocks analytically by solving the differential equations obtained by acting with the Casimirs of the global subalgebras inside the four point function. These global blocks agree with the general SGC blocks in the limit of large central charge. We comment on possible applications to supersymmetric BMS$_3$ invariant field theories and flat holography.

hep-th↗

arXiv2017

The nuts and bolts of the BMS Bootstrap

In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of crossing symmetry in 4-point functions that are constrained by symmetry. The BMS bootstrap equation is formulated and then analytic expressions for BMS blocks are constructed by looking at the limit of large central charges. These results are also applicable to 2d Galilean Conformal Field Theories through the isomorphism between the BMS3 and 2d Galilean Conformal Algebras. We recover our previously obtained results in the non-relativistic limit of the corresponding ones in 2d relativistic CFTs. This provides a comprehensive check of our previous analysis. We also explore the chiral limit of BMS3 where the BMS algebra reduces to a single copy of the Virasoro algebra and show that our analysis is consistent with earlier work in this direction.

hep-th↗

arXiv2016

The BMS Bootstrap

We initiate a study of the bootstrap programme for field theories with BMS symmetry. Specifically, we look at two-dimensional field theories with BMS3 symmetry and, using highest weight representations, we construct the BMS bootstrap equation by formulating the notion of crossing symmetry in the four-point functions of these field theories. In the limit of large central charges, we find analytic expressions for the BMS blocks that are the basic ingredients for the solution of the bootstrap equation. This constitutes, to the best of our knowledge, the first example of the formulation and significant steps towards the solution of a bootstrap equation in a theory which is not a relativistic conformal field theory.

hep-th↗

arXiv2015

Quantum theory of nonlocal nonlinear Schrodinger equation

Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.

quant-ph↗

arXiv2014

Trivalent graphs, volume conjectures and character varieties

The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to $U_q(\fraksl_2)$ colored quantum invariants of the theta and tetrahedron graph. The $\SL(2,\bC)$ character variety of the fundamental group of the complement of a trivalent graph with $E$ edges in $S^3$ is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus $g=E/3+1$. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the $q$-holonomic difference equation of the quantum invariants provides the quantization of the character variety.

math.GT↗

arXiv2014

Colored Kauffman Homology and Super-A-polynomials

We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super-A-polynomials is extended in order to encompass two-parameter deformations of PSL(2,C) character varieties.

hep-th↗

arXiv2013

Multiplicity-free quantum 6j-symbols for U_q(sl_N)

We conjecture a closed form expression for the simplest class of multiplicity-free quantum 6j-symbols for U_q(sl_N). The expression is a natural generalization of the quantum 6j-symbols for U_q(sl_2) obtained by Kirillov and Reshetikhin. Our conjectured form enables computation of colored HOMFLY polynomials for various knots and links carrying arbitrary symmetric representations.

hep-th↗

arXiv2013

Colored HOMFLY polynomials from Chern-Simons theory

We elaborate the Chern-Simons field theoretic method to obtain colored HOMFLY invariants of knots and links. Using multiplicity-free quantum 6j-symbols for U_q(sl_N), we present explicit evaluations of the HOMFLY invariants colored by symmetric representations for a variety of knots, two-component links and three-component links.

hep-th↗

arXiv2013

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

hep-th↗

arXiv2013

SU(N) quantum Racah coefficients & non-torus links

It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory. Using isotopy equivalence of SU(N) Chern-Simons functional integrals over three balls with one or more $S^2$ boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N) representations. Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links. These results are useful for verifying conjectures in topological string theory.

hep-th↗

arXiv2012

Reformulated invariants for non-torus knots and links

Using the Racah coefficients in our earlier paper arXiv:1107.3918, we explicitly write the Chern-Simons field theory invariants for many non-torus knot and links. Further, we have tabulated the reformulated invariants which agrees with the Ooguri-Vafa conjecture for knots and Labastida-Marino-Vafa conjecture for links.

hep-th↗