1,721,028 research outputs found
A model for a light graviphoton
No full textWe describe an explicit N=2 supergravity model where an arbitrarily light vector boson ("graviphoton") is coupled, with typical gravitational strength to matter hypermultiplets, possessing unbroken gauge interactions as well. We discuss: i) the mass and the couplings of the graviphoton; ii) the consistency of its coupling to a mass generated by the Higgs mechanism; iii) the actual composition of the graviphoton in terms of the original vector fields of the Lagrangian (e.g. its mixing with the photon)
Stochastic processes in lattice (extended) supersymmetry
No full textWe show that ungauged N = 2 supersymetric models can be put on the (hamiltonian) lattice in such a way as to preserve a subalgebra of supersymmetry large enough to ensure the existence of the Nicolai mapping. The models can be interpreted as stochastic systems described by Langevin equations. We describe both Wilson and Susskind versions of the model. In two dimensions everything seems fine, but in 4D, one expects, on general grounds, that the continuum limit will be either trivial or non-Lorentz invarian
Categorical Webs and S-Duality in 4d N=2 QFT
No full textWe review the categorical approach to the BPS sector of a 4d N=2 QFT, clarifying many tricky issues and presenting a few novel results. To a given N=2 QFT one associates several triangulated categories: they describe various kinds of BPS objects from different physical viewpoints (e.g. IR versus UV). These diverse categories are related by a web of exact functors expressing physical relations between the various objects/pictures. A basic theme of this review is the emphasis on the full web of categories, rather than on what we can learn from a single description. A second general theme is viewing the cluster category as a sort of categorification' of 't Hooft's theory of quantum phases for a 4d non-Abelian gauge theory. The S-duality group is best described as the auto-equivalences of the full web of categories. This viewpoint leads to a combinatorial algorithm to search for S-dualities of the given N=2 theory. If the ranks of the gauge and flavor groups are not too big, the algorithm may be effectively run on a laptop. This viewpoint also leads to a clearer view of 3d mirror symmetry. For class S theories, all the relevant triangulated categories may also be constructed in terms of geometric objects on the Gaiotto curve, and we present the dictionary between triangulated categories and the WKB approach of GMN. We also review how the VEV's of UV line operators are related to cluster characters
Homological S-Duality in 4d N=2 QFTs
No full textThe S[duality group S[double-struck](F) of a 4d N = 2 supersymmetric theory F is identified with the group of triangle equivalences of its cluster category C (F) modulo the subgroup acting trivially on the physical quantities. S[double-struck](F) is a discrete group commensurable to a subgroup of the Siegel modular group Sp(2g,) (g being the dimension of the Coulomb branch). This identification reduces the determination of the S-duality group of a given N = 2 theory to a problem in homological algebra. In this paper we describe the techniques which make the computation straightforward for a large class of N = 2 QFTs. The group S[double-struck](F) is naturally presented as a generalized braid group. The S-duality groups are often larger than expected. In some models the enhancement of S-duality is quite spectacular. For instance, a QFT with a huge S-duality group is the Lagrangian SCFT with gauge group SO(8) × SO(5)3 × SO(3)6 and half-hypermultiplets in the bi- and tri-spinor representations. We focus on four families of examples: the N = 2 SCFTs of the form (G,G"), Dp(G), and E r(1,1) (G), as well as the asymptoticallyfree theories (G, Ĥ) (which contain N = 2 SQCD as a special case). For the E r(1,1) (G) models we confirm the presence of the PSL(2,) S-duality group predicted by Del Zotto, Vafa and Xie, but for most models in this class S-duality gets enhanced to a larger group
FQHE and tt * geometry
Full text linkCumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy representation of the associated tt* geometry. In this paper we study the monodromy representation of the Vafa 4-susy model. Modulo some plausible assumption, we find that the monodromy representation factors through a Temperley-Lieb/Hecke algebra with q = ± exp (πi/ν) as predicted in [1]. The emerging picture agrees with the other predictions of [1] as well. The bulk of the paper is dedicated to the development of new concepts, ideas, and techniques in tt* geometry which are of independent interest. We present several examples of these geometric structures in various contexts
Galois covers of N=2 BPS spettra and quantum monodromy
No full textThe BPS spectrum of many 4d N = 2 theories may be seen as the (categorical) Galois cover of the BPS spectrum of a different 4d N = 2 model. The Galois group G acts as a physical symmetry of the covering N = 2 model. The simplest instance is SU(2) SQCD with Nf = 2 quarks, whose BPS spectrum is a Z2-cover of the BPS spectrum of pure SYM. More generally, N =2 SYM with simply-laced gauge group G admits Zk-covers for all k N;e.g. the Z2-cover of SO(8) SYM is SO(8) SYM coupled to two copies of the E6 Minahan-Nemeshanski SCFT. Galois covers simplify considerably thecomputationoftheBPSspectrumatG-symmetric points, in both finite and infinite chambers. When the covering and quotient QFTs admit a geometric engineering, say for class S models, the categorical spectral cover may be realized as a covering map in the geometry. A particularly nice instance is when the spectral Galois cover is induced by a modular cover of principal modular curves, X (NM) → X (M), or, more generally, by regular Grothendieck's dessins d'enfants; the BPS spectra of the corresponding N =2 QFTs have magic properties. The Galois covers allow to study effectively the action of the quantum (half)monodromy K(q)of4d N = 2 QFTs. We present several examples and applications of the spectral covering philosophy
Special arithmetic of flavor
Full text linkAbstract We revisit the classification of rank-1 4d N=2 QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-Néron model maps the space of non-trivial rank-1 special geometries to the well-known moduli of pairs (ε, F ∞) where E is a relatively minimal, rational elliptic surface with section, and F ∞ a fiber with additive reduction. Requiring enough Seiberg-Witten differentials yields a condition on (ε, F ∞) equivalent to the “safely irrelevant conjecture”. The Mordell-Weil group of E (with the Néron-Tate pairing) contains a canonical root system arising from (−1)-curves in special position in the Néron-Severi group. This canonical system is identified with the roots of the flavor group F: the allowed flavor groups are then read from the Oguiso-Shioda table of Mordell-Weil groups. Discrete gaugings correspond to base changes. Our results are consistent with previous work by Argyres et al
Geometric classification of 4d N=2 SCFTs
Full text linkAbstract The classification of 4d N=2 SCFTs boils down to the classification of conical special geometries with closed Reeb orbits (CSG). Under mild assumptions, one shows that the underlying complex space of a CSG is (birational to) an affine cone over a simply-connected ℚ-factorial log-Fano variety with Hodge numbers h p,q = δ p,q . With some plausible restrictions, this means that the Coulomb branch chiral ring is a graded polynomial ring generated by global holomorphic functions u i of dimension Δ i . The coarse-grained classification of the CSG consists in listing the (finitely many) dimension k-tuples {Δ1 , Δ2 , ⋯ , Δ k } which are realized as Coulomb branch dimensions of some rank-k CSG: this is the problem we address in this paper. Our sheaf-theoretical analysis leads to an Universal Dimension Formula for the possible {Δ1 , ⋯ , Δ k }’s. For Lagrangian SCFTs the Universal Formula reduces to the fundamental theorem of Springer Theory. The number N(k) of dimensions allowed in rank k is given by a certain sum of the Erdös-Bateman Number-Theoretic function (sequence A070243 in OEIS) so that for large k Nk=2ζ2ζ3ζ6k2+ok2. In the special case k = 2 our dimension formula reproduces a recent result by Argyres et al. Class Field Theory implies a subtlety: certain dimension k-tuples {Δ1 , ⋯ , Δ k } are consistent only if supplemented by additional selection rules on the electro-magnetic charges, that is, for a SCFT with these Coulomb dimensions not all charges/fluxes consistent with Dirac quantization are permitted. Since the arguments tend to be abstract, we illustrate the various aspects with several concrete examples and perform a number of explicit checks. We include detailed tables of dimensions for the first few k’s
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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