Is toric duality a Seiberg-like duality in (2+1)-d ?

We show that not all $(2+1)$ dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos ${\cal{C}}_3$, ${\cal{C}}_5$ and ${\cal{B}}_2$. We find that the indices for the two toric phases of Fano ${\cal{B}}_2$ do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.Comment: 21 pages, 7 figures, to be published in JHE

Partial resolution of complex cones over Fano B{\cal{B}}

In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2-branes probing the singularities of special kind of Calabi-Yau four-folds which were complex cones over toric Fano $\mathbb{P}^3$, ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data of $\mathbb{C}^4$ and Fano $\mathbb{P}^3$ can be embedded inside the toric data of Fano ${\cal{B}}$ theories. This method indirectly justfies that the two node quiver Chern-Simons theories corresponding to $\mathbb{C}^4$, Fano $\mathbb{P}^3$ and their orbifolds can be obtained by higgsing matter fields of the three node parent quiver corresponding to Fano ${\cal{B}}_1$, ${\cal{B}}_2$, ${\cal{B}}_3$, ${\cal{B}}_4$ three-folds.Comment: 22 pages, 8 figure

Constraints on CP-violating gauge-Higgs operators

We consider the most general set of $SU(2) \times U(1)$ invariant CP-violating operators of dimension six, which contribute to $VVh$ interactions ($V = W, Z, \gamma$). Our aim is to constrain any CP-violating new physics above the electroweak scale via the effective couplings that arise when such physics is integrated out. For this purpose, we use, in turn, electroweak precision data, global fits of Higgs data at the Large Hadron Collider and the electric dipole moments of the neutron and the electron. We thus impose constraints mainly on two-parameter and three-parameter spaces. We find that the constraints from the electroweak precision data are the weakest. Among the existing Higgs search channels, considerable constraints come from the diphoton signal strength. We note that potential contribution to $h \rightarrow \gamma Z$ may in principle be a useful constraining factor, but it can be utilized only in the high energy run. The contributions to electric dipole moments mostly lead to the strongest constraints, though somewhat fine-tuned combinations of more than one parameter with large magnitudes are allowed. We also discuss constraints on gauge boson trilinear couplings which depend on the parameters of the CP-violating operators .Comment: Published in Physical Review

Reconstructing a light pseudoscalar in the Type-X Two Higgs Doublet Model

We investigate the detectability as well as reconstructibility of a light pseudoscalar particle $A$, of mass in the 50 - 60 GeV range, which is still allowed in a Type-X (lepton-specific) two-Higgs doublet scenario. Such a pseudoscalar can be pair-produced in the decay $h\to AA$ of the 125 GeV scalar $h$. The light pseudoscalar in the aforementioned range, helpful in explaining the muon anomalous magnetic moment, has not only substantial branching ratio in the $\tau^+\tau^-$ channel but also one of about $0.35\%$ in the $\mu^+\mu^-$ final state. We show how to faithfully reconstruct the $A$ mass using the $\mu^+\mu^-$ mode, and establish the existence of a pseudoscalar around 50 - 60 GeV, using the process $pp\to h \to AA\to \mu^+\mu^-\,\tau^+\tau^-$. This is the most reliable way of reconstructing the light $A$ mass, and is possible for an integrated luminosity of about $100~\rm{fb}^{-1}$ or less at 14 TeV, with a statistical significance that amounts to discovery.Comment: v2: version published in PLB. 13 pages, 6 figures, 3 table

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 R\'enyi 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 R\'enyi 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.Comment: 38 pages, 24 figures & 15 tables; v2: Introduction & Conclusion modified, new subsection added in section 3, three new references added; matches published versio

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 R\'enyi 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 R\'enyi 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 R\'enyi 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 $n$.Comment: 31 pages, 5 figure

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.Comment: 16 pages, 1 figures, published versio