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Numerical Evidence for a p_x - ip_y Paired Fractional Quantum Hall State at ν = 12/5
Get PDFWe provide numerical evidence supporting a Bonderson–Slingerland (BS) non-Abelian hierarchy state as a candidate for the observed ν = 12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν = 12/5 quantum Hall state with shift S = 2 matching that of the BS state. The exact ground-state of the Coulomb interaction state on the sphere is shown to have large overlap with the BS ground-state trial wavefunction. The analysis of the BS states is extended to hierarchical descendants of general paired states in the weak-pairing phase at ν = 5/2
An Irish manuscript at Glin Castle
Get PDFDescription of an eighteenth-century Irish manuscript from Co. Limeric
Free Resolutions via Gröbner Bases
Get PDFIn many different settings (associative algebras, commutative algebras, operads, dioperads), it is possible to develop the machinery of Gröbner bases; it allows to find a “monomial replacement” for every object in the corresponding category. The main goal of this article is to demonstrate how this machinery can be used for the purposes of homo-logical algebra. More precisely, we define combinatorial resolutions in the monomial case and then show how they can be adjusted to be used in the general homogeneous case. We also discuss a way to make our monomial resolutions minimal. For associative algebras, we recover a well known construction due to Anick. Various applications of these results are presented, including a new proof of Hoffbeck’s PBW criterion, a proof of Koszulness for a class of operads coming from commutative algebras, and a homology computation for the operad of Batalin–Vilkovisky algebras
Condensate-induced transitions between topologically ordered phases
Get PDFWe investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have non-integer quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories and we find that there is a beautiful connection between quantum group sym-metry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail
Applications of the superconformal index for protected operators and q-hypergeometric identities to N = 1 dual theories
Get PDFThe results of Römelsberger for a N = 1 superconformal index counting protected operators, satisfying a BPS condition and which cannot be combined to form long multiplets, are analysed further. The index is expressible in terms of single particle superconformal characters for N = 1 scalar and vector multiplets. For SQCD, involving SU(N_c) gauge groups and appropriate numbers of flavours N_f , the formula used to construct the index may be proved to give identical results for theories linked by Seiberg duality using recently proved theorems for q-series elliptic hyper-geometric integrals. The discussion is also extended to Kutasov-Schwimmer dual theories in the large N_c , N_f limit and to dual theories with Sp(N) and SO(N) gauge groups. For the former, a transformation identity for elliptic hypergeometric integrals directly verifies that the index is the same for the electric and magnetic theories. For SO(N) theories the corresponding result may also be obtained from the same basic identity. An expansion of the index to several orders is also obtained in a form where the detailed protected operator content may be read off. Relevant mathematical results are reviewed
Constraints from CMB on Spacetime Noncommutativity and Causality Violation
Get PDFWe try to constrain the noncommutativity length scale of the theoretical model given in [1] using the observational data from ACBAR, CBI and five year WMAP. The noncommutativity parameter is not constrained by WMAP data, however ACBAR and CBI data restrict the lower bound of its energy scale to be around 10 TeV. We also derive an expression for the amount of non-causality coming from spacetime noncommutativity for the fields of primordial scalar perturbations that are space-like separated. The amount of causality violation for these field fluctuations are direction dependent
A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
Get PDFWe present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms of finite dimensional matrices, calculate the spectrum and explicitly exhibit the Dirac eigenspinors. To our knowledge the spin c spectrum for CP^n with n ≥ 3 is new
Magnetic charge lattices, moduli spaces and fusion rules
Get PDFWe analyze the set of magnetic charges carried by smooth BPS monopoles in Yang-Mills-Higgs theory with arbitrary gauge group G spontaneously broken to a subgroup H. The charges are restricted by a generalized Dirac quantization condition and by an inequality due to Murray. Geometrically, the set of allowed charges is a solid cone in the coroot lattice of G, which we call the Murray cone. We argue that magnetic charge sectors correspond to points in the Murray cone divided by the Weyl group of H; hence magnetic charge sectors are labelled by dominant integral weights of the dual group H* . We define generators of the Murray cone modulo Weyl group, and interpret the monopoles in the associated magnetic charge sectors as basic; monopoles in sectors with decomposable charges are interpreted as composite configurations. This interpretation is supported by the dimensionality of the moduli spaces associated to the magnetic charges and by classical fusion properties for smooth monopoles in particular cases. Throughout the paper we compare our findings with corresponding results for singular monopoles recently obtained by Kapustin and Witten