236 research outputs found
Exact results for two-dimensional N=2 supersymmetric theories (an introduction to the tt* technique)
No full textExact Results for Two-Dimensional N=2 Supersymmetric Theories, S. Cecotti; Developments in 2D String Theory, A. Jevicki; A String Project in Multicolour QCD, V. Kazakov; Matrix Models and String Theory, I. Klebanov; Black Hole Evaporation and Quantum Gravity, H. Verlinde; Barriers in Quantum Gravity, J. Ambjorn; Two-Dimensional Black Hole and Nonperturbative String Theory, A. Dhar; U(N) Gauge Theory and Lattice Strings, I. Kostov; Applications of 0(d,d) Transformations to Generate New Geometries, J. Maharana; Quantization of Mirror Symmetry, H. Ooguri; W-Strings 93, C. Pope; and other papers
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
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
Higher S-dualities and Shephard-Todd groups
Get PDFAbstract: Seiberg and Witten have shown that in N=2 SQCD with Nf = 2Nc = 4 the S-duality group PSL2ℤ acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2 SCFTs in which SU(2) SYM is coupled to strongly-interacting non-Lagrangian matter: their matter charges are weights of E6, E7 and E8 instead of Spin(8). The S-duality group PSL2ℤ acts on these weights: what replaces Spin(8) triality for the E6, E7, E8root lattices? In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL2ℤ factorizes trough the action of the exceptional Shephard-Todd groups G4 and G8 which should be seen as complex analogs of the usual triality group S3≃WeylA2. Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type. © 2015, The Author(s)
Cosmological attractor models and higher curvature supergravity
Get PDFWe study cosmological α-attractors in superconformal/supergravity models, where α is related to the geometry of the moduli space. For α = 1 attractors [1] we present a generalization of the previously known manifestly superconformal higher curvature supergravity model [2]. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic α-models [3] interpolate between the attractor point at α = 0 and generic chaotic inflation models at large α, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as the original theory or less, but at least one matter multiplet remains. In the context of these models, the detection of primordial gravity waves will provide information on the curvature of the inflaton submanifold of the Kähler manifold, and we will learn if the inflaton is a fundamental matter multiplet, or can be replaced by a higher derivative curvature excitation. © 2014 The Author(s)
Homogeneous Kähler manifolds and T algebras in N = 2 supergravity and superstrings
No full textMotivated by the problem of the moduli space of superconformal theories, we classify all the (normal) homogeneous Kähler spaces which are allowed in the coupling of vector multiplets to N=2 SUGRA. Such homogeneous spaces are in one-to-one correspondence with the homogeneous quaternionic spaces (≠HHn) found by Alekseevskii. There are two infinite families of homogeneous non-symmetric spaces, each labelled by two integers. We construct explicitly the corresponding supergravity models. They are described by a cubic function F, as in flat-potential models. They are Kähler-Einstein if and only if they are symmetric. We describe in detail the geometry of the relevant manifolds. They are Siegel (bounded) domains of the first type. We discuss the physical relevance of this class of bounded domains for string theory and the moduli geometry. Finally, we introduce the T-algebraic formalism of Vinberg to describe in an efficient way the geometry of these manifolds. The homogeneous spaces allowed in N=2 SUGRA are associated to rank 3 T-algebras in exactly the same way as the symmetric spaces are related to Jordan algebras. We characterize the T-algebras allowed in N=2 supergravity. They are those for which the ungraded determinant is a polynomial in the matrix entries. The Kähler potential is simply minus the logarithm of this "naive" determina
Geometric classification of 4d N=2 SCFTs
Get PDFAbstract 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
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)
Supersymmetric Born-Infeld Lagrangians
No full textThe supersymmetric completion of four-dimensional Born-Infeld-type actions is established by means of superspace techniques for the construction of higher-curvature invariants. The coupling of these actions to supergravity is also obtained. These results are relevant for the understanding of the full effective action of superstring theorie
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
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