arXiv subjects

Siddharth Dwivedi

Publications and source records attributed to Siddharth Dwivedi.

At least 19 recordsLinked to original sources

arXiv2026

Generalized momentum operators from Fourier transform correspondence

In this work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting from the Fourier transform (FT) relationship, we present a Hermitian generalization of the canonical momentum operator in position space. The action of the generalized operator is found to generate a local flow accompanied by position-dependent rescaling, rather than a global translation. Explicit eigenfunctions are obtained for representative cases and are shown to possess a well-defined limit to the plane-wave solution in QM. As an illustration, the infinite square well problem is solved using the generalized operator, yielding a deformed spectrum that has a smooth limit to the standard QM result.

quant-ph↗

arXiv2026

Large-party limit of topological entanglement entropy in Chern-Simons theory

We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group $G$ and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{dm,dn}$ torus link complements, which is a $d$-party pure quantum state, and analyze its large-party limit, i.e., $d\to \infty$ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of $\ln |Z_G|$, where $|Z_G|$ is the order of the center of the group $G$. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and $T_{d,dn}$ torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical ($k \to \infty$) limit of the entropies after taking the large-party limit for this particular example.

hep-th↗

arXiv2025

Analyzing reduced density matrices in SU(2) Chern-Simons theory

We investigate the reduced density matrices obtained for the quantum states in the context of 3d Chern-Simons theory with gauge group SU(2) and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{p,p}$ torus link complements, which is a $p$-party pure quantum state. The reduced density matrices are obtained by taking the $(1|p-1)$ bi-partition of the total system. We show that the characteristic polynomials of these reduced density matrices are monic polynomials with rational coefficients.

hep-th↗

arXiv2024

Topological entanglement and number theory

The recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The purpose of this note is twofold. First, we introduce a $q$-deformed version of the Witten zeta function using the Chern-Simons theory at level $k$. We analyze the large $k$ limit of this function and show that it converges to an integer multiple of the classical Witten zeta function of $G$, where the integer multiple is precisely the order of the center of the group. This analysis provides an alternative way to compute the classical zeta functions, and we present some examples. Next, we study the quantum state associated with the $S^3$ complement of torus links of type $T_{p,p}$ and show that we can write the R\'enyi entropies at finite $k$ in terms of $q$-deformed Witten zeta functions. Using our first result, we obtain the $k \to \infty$ limit of the R\'enyi entropies and find that the entropies converge to finite values, which can be written in terms of the classical Witten zeta functions evaluated at positive integers. Since Witten zeta functions naturally appear in the symplectic volumes of moduli spaces of flat connections on Riemann surfaces, we give a geometric interpretation of the $k \to \infty$ limit of the R\'enyi and entanglement entropies in terms of these volumes. The results of this paper reveal an intriguing connection between topological entanglement, number-theoretic structures arising from Witten zeta functions, and the geometry of moduli spaces.

hep-th↗

arXiv2024

Knot-Quiver correspondence for double twist knots

We obtain a quiver representation for a family of knots called double twist knots $K(p,-m)$. Particularly, we exploit the reverse engineering of Melvin-Morton-Rozansky(MMR) formalism to deduce the pattern of the charge matrix for these quivers.

hep-th↗

arXiv2024

Exploring topological entanglement through Dehn surgery

We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by our earlier work on topological entanglement and the reduced density matrix $σ$ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix $σ$ becomes equal to the $\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use the SnapPy program and numerical techniques to show this equivalence up to the leading order. We have given explicit results for all hyperbolic knots $\mathcal{K}$ up to six crossings.

hep-th↗

arXiv2022

Discovery prospects of a light charged Higgs near the fermiophobic region of Type-I 2HDM

Determining if the SM-like Higgs is part of an extended Higgs sector is the most important question to be asked after discovery. A light charged Higgs boson with mass smaller than the sum of top and bottom quarks is naturally allowed in Type-I two Higgs doublet model and can be produced in association with neutral scalars for large parts of parameter space at the LHC. Such low mass charged scalars typically have dominant decays to the fermionic modes viz. $τν$ and $c s$. However in the presence of light neutral scalar ($φ$), the charged Higgs boson has a substantial branching fraction into the bosonic decay modes $H^{\pm} \to W^{(*)} φ$. Identifying the heavier neutral Higgs ($H$) with the observed 125 GeV Higgs and working in the limit $M_{H^\pm} \approx M_A$, we examine charged Higgs production and decay in the bosonic mode $p p \to H^\pm h \to W^{(*)}h h$. The presence of two light Higgses ($h$) is then the key to identifying charged Higgs production. The light Higgs branching ratio is largely dominated by the $b\bar{b}$ mode except when close to the fermiophobic limit. Here, the rates into $b \bar b$ and $γγ$ can be comparable and we can use the $γγb\bar{b}$ signature. This signature is complementary to the $h h \to 4γ$ which has been previously discussed in literature. Using the lepton from the $W$ boson, we demonstrate with a cut-and-count analysis that both the new light neutral Higgs as well as charged Higgs can be probed with reasonable significance at 13.6 TeV LHC with 300-3000 fb$^{-1}$ of integrated luminosity.

hep-ph↗

arXiv2022

Searching exotic Higgs bosons at the LHC

We analyse in a model independent way the possibilities of digging out neutral exotic Higgs states, should they exist endowed with unconventional couplings with ordinary matter and gauge fields, at the 14 TeV run of the Large Hadron Collider (LHC), adding some comparative studies for 13.6 and 13 TeV runs. Flavor models, based on some discrete symmetry groups, with extended scalar sectors are known to yield exotic spin-0 states, both CP-even and CP-odd, with purely flavor off-diagonal Yukawa couplings. The gauge interaction of one such CP-even state is also unusual that, unlike the Standard Model Higgs boson, it does not couple to gauge boson pairs. Such unconventional properties immune these exotic states from receiving traditional collider and electroweak constraints, and hence those states could be light. Without committing to any specific model, exploiting their peculiar Yukawa and gauge properties, we explore the discovery potential of those exotic Higgs states through some interesting topologies by figuring out some specific kinematic variables that suppress the backgrounds.

hep-ph↗

arXiv2022

Exploring the orthosymplectic zoo

We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for computing the local Coulomb branch Hilbert series for quivers involving bad USp(2) gauge nodes.

hep-th↗

arXiv2021

Topological entanglement and hyperbolic volume

The entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the Rényi entropy of index $m$, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with $S^3$ complements of a two-component link which is a connected sum of a knot $\mathcal{K}$ and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the $m$-moment of the reduced density matrix as a three-manifold invariant $Z(M_{\mathcal{K}_m})$, which is the partition function of $M_{\mathcal{K}_m}$. Here $M_{\mathcal{K}_m}$ is a closed 3-manifold associated with the knot $\mathcal K_m$, where $\mathcal K_m$ is a connected sum of $m$-copies of $\mathcal{K}$ (i.e., $\mathcal{K}\#\mathcal{K}\ldots\#\mathcal{K}$) which mimics the well-known replica method. We analyse the partition functions $Z(M_{\mathcal{K}_m})$ for SU(2) and SO(3) gauge groups, in the limit of the large Chern-Simons coupling $k$. For SU(2) group, we show that $Z(M_{\mathcal{K}_m})$ can grow at most polynomially in $k$. On the contrary, we conjecture that $Z(M_{\mathcal{K}_m})$ for SO(3) group shows an exponential growth in $k$, where the leading term of $\ln Z(M_{\mathcal{K}_m})$ is the hyperbolic volume of the knot complement $S^3\backslash \mathcal{K}_m$. We further propose that the Rényi entropies associated with SO(3) group converge to a finite value in the large $k$ limit. We present some examples to validate our conjecture and proposal.

hep-th↗

arXiv2021

Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers

We study the moduli space of 3d $\mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $\mathcal{N}=1$ superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

hep-th↗

arXiv2020

Semiclassical limit of topological Rényi entropy in $3d$ Chern-Simons theory

We study the multi-boundary entanglement structure of the state associated with the torus link complement $S^3 \backslash T_{p,q}$ in the set-up of three-dimensional SU(2)$_k$ Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of $k \to \infty$. We present a detailed analysis for several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large $k$ limiting value of the Rényi entropy of torus links of type $T_{p,pn}$ is the sum of two parts: (i) the universal part which is independent of $n$, and (ii) the non-universal or the linking part which explicitly depends on the linking number $n$. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological $2d$ Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large $k$ limits of the entanglement entropy and the minimum Rényi entropy for torus links $T_{p,pn}$ can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of $T_{p,pn}$ link in the double scaling limit of $k \to \infty$ and $n \to \infty$ and propose that the entropies converge in the double limit as well.

hep-th↗

arXiv2020

Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in arXiv:2004.04082, by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and $\mathbb{Z}_2$ gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.

hep-th↗

arXiv2020

Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group $G$. The states in (1+1)-$d$ are associated with Riemann surfaces of genus $g$ with multiple $S^1$ boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-$d$, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple $T^2$. We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. $\text{EE}(G_1 \times G_2) = \text{EE}(G_1)+\text{EE}(G_2)$. Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space.

hep-th↗

arXiv2020

Associated $Z^\prime$ production in the flavorful $U(1)$ scenario for $R_{K^{(*)}}$

The flavorful $Z^\prime$ model with its couplings restricted to the left-handed second generation leptons and third generation quarks can potentially resolve the observed anomalies in $R_K$ and $R_{K^*}$. After examining the current limits on this model from various low-energy processes, we probe this scenario at 14 TeV high-luminosity run of the LHC using two complementary channels: one governed by the coupling of $Z'$ to $b$-quarks and the other to muons. We also discuss the implications of the latest LHC high mass resonance searches in the dimuon channel on the model parameter space of our interest.

hep-ph↗

arXiv2019

Entanglement on multiple $S^2$ boundaries in Chern-Simons theory

Topological entanglement structure amongst disjoint torus boundaries of three manifolds have already been studied within the context of Chern-Simons theory. In this work, we study the topological entanglement due to interaction between the quasiparticles inside three-manifolds with one or more disjoint $S^2$ boundaries in SU($N$) Chern-Simons theory. We focus on the world-lines of quasiparticles (Wilson lines), carrying SU($N$) representations, creating four punctures on every $S^2$. We compute the entanglement entropy by partial tracing some of the boundaries. In fact, the entanglement entropy depends on the SU($N$) representations on these four-punctured $S^2$ boundaries. Further, we observe interesting features on the GHZ-like and W-like entanglement structures. Such a distinction crucially depends on the multiplicity of the irreducible representations in the tensor product of SU($N$) representations.

hep-th↗

arXiv2018

Reconstructing heavy Higgs boson masses in Type X Two-Higgs Doublet Model with a light pseudoscalar

We analyze the prospects of reconstructing the mass of a heavy charged Higgs boson %have been analyzed in the context of a Type X two-Higgs doublet model where a light pseudoscalar $A$ in the mass range $40-60$ GeV is phenomenologically allowed, and is in fact favoured if one wants to explain the muon anomalous magnetic moment. The associated production of charged Higgs with the pseudoscalar $A$ and subsequent decay of the charged Higgs into a $W$ and $A$, is found to be our relevant channel. The branching ratio for $H^+ \to W^+ A$ with $M_{H^+} \sim 200$ GeV, is close to 50\%. The hadronic decay of the $W$ boson, coupled with the leptonic decays of $A$ into a tau and muon pair, help in identifying the charged Higgs. The neutral heavy Higgs, being degenerate with the charged Higgs for most of the allowed parameter space of the model, also contributes to similar final states. Thus both of these particles are reconstructed within a band of about 10 GeV.

hep-ph↗

arXiv2018

Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups

We study the entanglement for a state on linked torus boundaries in $3d$ Chern-Simons theory with a generic gauge group and present the asymptotic bounds of Rényi entropy at two different limits: (i) large Chern-Simons coupling $k$, and (ii) large rank $r$ of the gauge group. These results show that the Rényi entropies cannot diverge faster than $\ln k$ and $\ln r$, respectively. We focus on torus links $T(2,2n)$ with topological linking number $n$. The Rényi entropy for these links shows a periodic structure in $n$ and vanishes whenever $n = 0 \text{ (mod } \textsf{p})$, where the integer $\textsf{p}$ is a function of coupling $k$ and rank $r$. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in $n$.

hep-th↗