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### Browsing by Author "Tanzini, Alessandro"

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Item Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory(2006-11-09T10:57:36Z) Griguolo, Luca; Seminara, Domenico; Szabo, Richard J.; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.Show more Item The complete one-loop spin chain for N=2 Super-Yang-Mills(2007-10-29T14:28:13Z) Di Vecchia, Paolo; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.Show more Item Computing Amplitudes in topological M-theory(2006-12-07T16:26:28Z) Bonelli, Giulio; Tanzini, Alessandro; Zabzine, Maxim; Mathematics; Mathematical PhysicsShow more We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. In particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.Show more Item Instanton counting on Hirzebruch surfaces(2008-09-05T18:06:43Z) Bruzzo, Ugo; Poghossian, Rubik; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.Show more Item Instantons on ALE spaces and Super Liouville Conformal Field Theories(SISSA, 2011-06-13) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsShow more We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Show more Item Instantons on ALE spaces and Super Liouville Conformal Field Theories(SISSA, 2011-06-13) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsShow more We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Show more Item The Liouville side of the Vortex(SISSA, 2011-07-11) Bonelli, Giulio; Tanzini, Alessandro; Zhao, Jian; MathematicsShow more We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.Show more Item Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories(2010-03-02T08:00:49Z) Santachiara, Raoul; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more We identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.Show more Item N=1 superpotentials from multi-instanton calculus(2005) Fucito, Francesco; Morales, Jose F.; Poghossian, Rubik; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge theories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.Show more Item N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae(SISSA, 2013-02-05) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Yagi, Futoshi; MathematicsShow more We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.Show more Item N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae(SISSA, 2012-08-03) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Yagi, Futoshi; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsShow more We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety. We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.Show more Item On topological M-theory(2005) Bonelli, Giulio; Tanzini, Alessandro; Zabzine, Maxim; Mathematics; Mathematical PhysicsShow more We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds.Show more Item Quantum Hitchin Systems via beta-deformed Matrix Models(SISSA, 2011-04-20) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsShow more We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.Show more Item Quantum Hitchin Systems via beta-deformed Matrix Models(SISSA, 2011-05-17) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsShow more We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.Show more Item Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry(2005) Baulieu, Laurent; Bossard, Guillaume; Tanzini, Alessandro; Mathematics; Mathematical PhysicsShow more The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting "equivariant topological field theory" corresponds to the twist of super Yang-Mills theory on omega backgrounds.Show more Item Wild Quiver Gauge Theories(SISSA, 2011-12-15) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsShow more We study N=2 supersymmetric SU(2) gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional A_1 (2,0) theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.Show more