Related papers: A Spectral Gap Theorem in $SU(d)$
We conjecture a formula for the Schur index of N=2 four-dimensional theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS…
In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf…
In this paper we analyze various half-BPS defects in a general three dimensional N=2 supersymmetric gauge theory T. They correspond to closed paths in SUSY parameter space and their tension is computed by evaluating period integrals along…
In this paper, we study spectrally invariant subalgebras of uniform Roe algebras for discrete groups with subexponential growth. For a group $G$ with subexponential growth and satisfying property $P$, we construct a class of subalgebras…
The dark sector is postulated to be invariant under an $SU(2)$ gauge symmetry, spontaneously broken by a Higgs quadruplet to a conserved residual $Z_3 \times Z_2$ symmetry. The resulting dark matter phenomenology is studied.
A dark sector with non-abelian gauge symmetry provides a sound framework to justify stable dark matter (DM) candidates. We consider scalar fields charged under a $SU(N)$ gauge group, and show that the centre of $SU(N)$, the discrete…
We show that a new gauge group with one new scalar leads to automatically stable Dark Matter candidates. We consider theories where the Higgs phase is dual to the confined phase: it is known that SU(2) gauge theories with a scalar doublet…
The deformed double covering of E(2) group, denoted by $\tilde{E}_\kappa(2)$, is obtained by contraction from the $SU_\mu(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant…
This note provides a very short proof of a spectral gap independent property of the simultaneous iterations algorithm for finding the top singular space of a matrix. See Rokhlin-Szlam-Tygert-2009, Halko-Martinsson-Tropp-2011 and…
We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…
Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification…
We prove that that for all $\eps$, having cogrowth exponent at most $1/2+\eps$ (in base $2m-1$ with $m$ the number of generators) is a generic property of groups in the density model of random groups. This generalizes a theorem of…
In this paper, we investigate the relationship between frame bounds and spectral gaps. By introducing the notion of \emph{essential minimum(maximal) spectral gap}, we provide a local characterization of Landau's theorem \cite{Lan67}. As an…
The gauge group of strong and electroweak interactions in Nature could be any of the four that share the same Lie algebra, $SU(3)_c\times SU(2)_L\times U(1)_Y/Z_p\equiv G_p$ with $Z_p=\left\{Z_6,Z_3,Z_2,Z_1\right\}$. Each of these cases…
We construct spectral triples for the C^*-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There has been various approaches towards building a calculus on quantum spaces, but there seems to be very few…
It is proved that there exists an (omega-1,omega-1) Souslin gap in the Boolean algebra (L(nu)/Fin,subseteq^*_ae) for every nonseparable measure nu. Thus a Souslin, also known as destructible, (omega-1,omega-1) gap in P(N)/Fin can always be…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
We explore statistical properties of BPS q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of 3-manifolds Y. We discover that gaps between exponents in the q-series are statistically more…
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point…
We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph decoration. The resulting Hamiltonians can be viewed as…