50 research outputs found
Emergent Phase Space Description of Unitary Matrix Model
We show that large phases of a 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) ( 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 . Therefore, large 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 representations and hence different large states of
the theory in momentum space. We explicitly consider two examples : single
plaquette model with terms and Chern-Simons theory on . 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 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 -leptons + -jets + {\mbox{{E\!\!\!\!/_T}}} signals for
different choices of .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 and
(wino models), we focus on the pMSSM models where and 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 and . The modes
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 + jets (3b) + channel provide
the best limit on ( 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 phases of
Chern-Simons matter theory on . 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
affine Lie algebra, where as upper-cap phase corresponds to
integrable representations of 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 and . 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 . When , ( 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 . 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 `-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 . 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
-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