Emergent Phase Space Description of Unitary Matrix Model

We show that large $N$ phases of a $0$ dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about different phases of UMM is encoded in the geometry of droplets. These droplets are similar to phase space distributions of a unitary matrix quantum mechanics (UMQM) ($(0 + 1)$ dimensional) on constant time slices. We find that for a given UMM, it is possible to construct an effective UMQM such that its phase space distributions match with droplets of UMM on different time slices at large $N$. Therefore, large $N$ phase transitions in UMM can be understood in terms of dynamics of an effective UMQM. From the geometry of droplets it is also possible to construct Young diagrams corresponding to $U(N)$ representations and hence different large $N$ states of the theory in momentum space. We explicitly consider two examples : single plaquette model with $\text{Tr} U^2$ terms and Chern-Simons theory on $S^3$. We describe phases of CS theory in terms of eigenvalue distributions of unitary matrices and find dominant Young distributions for them.Comment: 52 pages, 15 figures, v2 Introduction and discussions extended, References adde

The Electroweak Sector of the pMSSM in the Light of LHC - 8 TeV and Other Data

Using the chargino-neutralino and slepton search results from the LHC in conjunction with the WMAP/PLANCK and $(g-2)_{\mu}$ data, we constrain several generic pMSSM models with decoupled strongly interacting sparticles, heavier Higgs bosons and characterized by different hierarchies among the EW sparticles. We find that some of them are already under pressure and this number increases if bounds from direct detection experiments like LUX are taken into account, keeping in mind the associated uncertainties. The XENON1T experiment is likely to scrutinize the remaining models closely. Analysing models with heavy squarks, a light gluino along with widely different EW sectors, we show that the limits on gluino mass are not likely to be below 1.1 TeV, if a multichannel analysis of the LHC data is performed. Using this light gluino scenario we further illustrate that in future LHC experiments the models with different EW sectors can be distinguished from each other by the relative sizes of the $n$-leptons + $m$-jets + {\mbox{{E\!\!\!\!/_T}}} signals for different choices of $n$.Comment: 52 pages, 14 figures; few references added; published in JHE

Reduced LHC constraints for higgsino-like heavier electroweakinos

As a sequel to our earlier work on wino-dominated $\tilde \chi_1^{\pm}$ and $\tilde \chi_2^{0}$ (wino models), we focus on the pMSSM models where $\tilde \chi_1^{\pm}$ and $\tilde \chi_{2,3}^{0}$ are either higgsino dominated (higgsino models) or admixtures of significant amount of higgsino and wino components (mixed models), with or without light sleptons. The LHC constraints in the trilepton channel are significantly weaker even in the presence of light sleptons, especially in the higgsino models, compared to those mostly studied by the LHC collaborations with wino-dominated $\tilde \chi_1^{\pm}$ and $\tilde \chi_2^{0}$. The modes $\tilde \chi_{2,3}^{0}\rightarrow h~\tilde\chi_1^{0}$ with large branching ratios (BRs) are more common in the higgsino models and may produce spectacular signal in the LHC Run-II. In a variety of higgsino and mixed models we have delineated the allowed parameter space due to the LHC constraints, the observed Dark Matter (DM) relic density of the universe, which gets contributions from many novel DM producing mechanisms i.e., the annihilation/coannihilation processes that lead to the correct range of relic density, and the precise measurement of the anomalous magnetic moment of the muon. In the higgsino models many new DM producing mechanisms, which are not allowed in the wino models, open up. We have also explored the prospects of direct and indirect detection of DM in the context of the LUX and IceCube experiments respectively. In an extended model having only light gluinos in addition to the electroweak sparticles, the gluinos decay into final states with multiple taggable b-jets with very large BRs. As a consequence, the existing ATLAS data in the $0l$ + jets (3b) + $E\!\!\!\!/_T$ channel provide the best limit on $m_{\tilde g}$ ($\approx$ 1.3 TeV). Several novel signatures of higgsino models for LHC Run-II and ILC have been identified.Comment: 55 pages, 13 figures, 10 tables. Version published in JHE

From Phase Space to Integrable Representations and Level-Rank Duality

We explicitly find representations for different large $N$ phases of Chern-Simons matter theory on $S^2\times S^1$. These representations are characterised by Young diagrams. We show that no-gap and lower-gap phase of Chern-Simons-matter theory correspond to integrable representations of $SU(N)_k$ affine Lie algebra, where as upper-cap phase corresponds to integrable representations of $SU(k-N)_k$ affine Lie algebra. We use phase space description of arXiv:0711.0133 to obtain these representations and argue how putting a cap on eigenvalue distribution forces corresponding representations to be integrable. We also prove that the Young diagrams corresponding to lower-gap and upper-cap representations are related to each other by transposition under level-rank duality. Finally we draw phase space droplets for these phases and show how information about eigenvalue and Young diagram descriptions can be captured in topologies of these droplets in a unified way.Comment: 37 pages, 10 figures, v2 Introduction extended, References adde

Flow of shear response functions in hyperscaling violating Lifshitz theories

We study the flow equations of the shear response functions for hyperscaling violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating exponents $z$ and $\theta$. Adapting the membrane paradigm approach of analysing response functions as developed by Iqbal and Liu, we focus specifically on the shear gravitational modes which now are coupled to the perturbations of the background gauge field. Restricting to the zero momenta sector, we make further simplistic assumptions regarding the hydrodynamic expansion of the perturbations. Analysing the flow equations shows that the shear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound of $\frac{1}{4\pi}$. When $z=d_i-\theta$, ($d_i$ being the number of spatial dimension in the dual field theory) the first-order correction to shear viscosity exhibits logarithmic scaling, signalling the emergence of a scale in the UV regime for this class of hvLif theories. We further show that the response function associated to the gauge field perturbations diverge near the boundary when $z>d_i+2-\theta$. This provides a holographic understanding of the origin of such a constraint and further vindicates results obtained in previous works that were obtained through near horizon and quasinormal mode analysis.Comment: Includes new subsection on Markovianity index and breakdown of hydrodynamic expansion; Matches with published version; 19 + 3 page

Near-Extremal Freudenthal Duality

Freudenthal duality is, as of now, the unique non-linear map on electric-magnetic (e.m.) charges which is a symmetry of the Bekenstein-Hawking entropy of extremal black holes in Maxwell-Einstein-scalar theories in four space-time dimensions. In this paper, we present a consistent generalization of Freudenthal duality to near-extremal black holes, whose entropy is obtained within a Jackiw-Teitelboim gravity upon dimensional reduction. We name such a generalization near-extremal Freudenthal duality. Upon such a duality, two near-extremal black holes with two different (and both small) temperatures have the same entropy when their e.m. charges are related by a Freudenthal transformation. By exploiting Descartes' rule of signs as well as Sturm's Theorem, we show that our formulation of the near-extremal Freudenthal duality is analytical and unique.Comment: 29 pages, 2 figure

Matrix Model for Riemann Zeta via its Local Factors

We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `$p$-iecemeal', in the sense that we consider each factor in the Euler product representation of the zeta function to first construct a UMM for each prime $p$. We are able to use its phase space description to write the partition function as the trace of an operator that acts on a subspace of square-integrable functions on the $p$-adic field. This suggests a Berry-Keating type Hamiltonian. We combine the data from all primes to propose a Hamiltonian and a matrix model for the Riemann zeta function.Comment: v2 1+42 pages, expanded with additional details and explanations, typos correcte