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A bstract We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n -particle amplitudes in planar N = 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4 , n ). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8, and find that the polytope C † 4 9 encodes all rational letters, and all square roots of the algebraic letters, of known nine-particle amplitudes.

A bstract We consider general 5d SU( N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G . Each node has SU( N i ) gauge group of general rank, Chern-Simons level κ i and additional w i fundamentals. When the total flavor number at each node is less than or equal to 2 N i − 2| κ i |, we give general rules under which the symmetries associated to instanton currents are enhanced to G × G or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as S 1 compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.

We give a general formulation of semi-direct gauge mediation of supersymmetry breaking where the messengers interact with the hidden sector only through a weakly gauged group. Using this general formulation, we provide an explicit proof that the MSSM gaugino masses are vanishing to leading order in the gauge couplings. On the other hand, the MSSM sfermion masses have, generically, a non-vanishing leading contribution. We discuss how such a mechanism can successfully be combined with other mediation schemes which give tachyonic sfermions, such as sequestered anomaly mediation and some direct gauge mediation models.

We compute a set of correlation functions of operator insertions on the 1 / 8 BPS Wilson loop in $$ \\mathcal{N}=4 $$ N = 4 SYM by employing supersymmetric localization, OPE and the Gram-Schmidt orthogonalization. These correlators exhibit a simple determinant structure, are position-independent and form a topological subsector, but depend nontrivially on the ’t Hooft coupling and the rank of the gauge group. When applied to the 1 / 2 BPS circular (or straight) Wilson loop, our results provide an infinite family of exact defect CFT data, including the structure constants of protected defect primaries of arbitrary length inserted on the loop. At strong coupling, we show precise agreement with a direct calculation using perturbation theory around the AdS 2 string worldsheet. We also explain the connection of our results to the “generalized Bremsstrahlung functions” previously computed from integrability techniques, reproducing the known results in the planar limit as well as obtaining their finite N generalization. Furthermore, we show that the correlators at large N can be recast as simple integrals of products of polynomials (known as Q -functions) that appear in the Quantum Spectral Curve approach. This suggests an interesting interplay between localization, defect CFT and integrability.

Abstract The partition functions of free bosons as well as fermions on AdS 2 are not smooth as a function of their masses. For free bosons, the partition function on AdS 2 is not smooth when the mass saturates the Breitenlohner-Freedman bound. We show that the expectation value of the scalar bilinear on AdS 2 exhibits a kink at the BF bound and the change in slope of the expectation value with respect to the mass is proportional to the inverse radius of AdS 2. For free fermions, when the mass vanishes the partition function exhibits a kink. We show that expectation value of the fermion bilinear is discontinuous and the jump in the expectation value is proportional to the inverse radius of AdS 2. We then show the supersymmetric actions of the chiral multiplet on AdS 2 × S 1 and the hypermultiplet on AdS 2 × S 2 demonstrate these features. The supersymmetric backgrounds are such that as the ratio of the radius of AdS 2 to S 1 or S 2 is dialled, the partition functions as well as expectation of bilinears are not smooth for each Kaluza-Klein mode on S 1 or S 2. Our observation is relevant for evaluating one-loop partition function in the near horizon geometry of extremal black holes.

A bstract In earlier work with N. Seiberg, we explored connections between monopole operators, the Coulomb branch modulus, and vortices for 3d, N =2 supersymmetric, U(1) k Chern-Simons matter theories. We here extend the monopole / vortex matching analysis, to theories with general matter electric charges. We verify, for general matter content, that the spin and other quantum numbers of the chiral monopole operators match those of corresponding BPS vortex states, at the top and bottom of the tower associated with quantizing the vortices’ Fermion zero modes. There are associated subtleties from non-normalizable Fermi zero modes, which contribute non-trivially to the BPS vortex spectrum and monopole operator matching; a proposed interpretation is further discussed here.

The chiral algebra of 4D $$\\mathcal{N}=4$$ SU( N ) super-Yang-Mills theory is an $$\\mathcal{N}=4$$ superconformal vertex operator algebra. We analyse the structure of this algebra by studying recursively the constraints that are required by the associativity of the operator product expansion. We find that the algebra is uniquely characterized by the central charge (which can take an arbitrary value), without any additional free parameter. Furthermore, the truncation pattern of the OPE coefficients suggests that the algebra cannot arise from the symmetric orbifold.

Abstract We compute the topologically twisted index for general N = 2 $$ \\mathcal{N}=2 $$ supersymmetric field theories on ℍ 2 × S 1 $$ {\\mathrm{\\mathbb{H}}}_2\\times {S}^1 $$ . We also discuss asymptotically AdS 4 magnetically charged black holes with hyperbolic horizon, in four-dimensional N = 2 $$ \\mathcal{N}=2 $$ gauged supergravity. With certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find precise agreement between the black hole entropy and the topologically twisted index, for ABJ M theories.

Abstract Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A 2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.