Michele Cirafici

Michele Cirafici
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Michele Cirafici

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High Energy Physics - Theory (18)
Mathematics - Algebraic Geometry (8)
Mathematical Physics (3)
Mathematics - Mathematical Physics (3)
Mathematics - Algebraic Topology (2)
Mathematics - Quantum Algebra (2)
Mathematics - Representation Theory (2)
Nonlinear Sciences - Exactly Solvable and Integrable Systems (1)

Publications Authored By Michele Cirafici

A large class of N=2 quantum field theories admits a BPS quiver description and the study of their BPS spectra is then reduced to a representation theory problem. In such theories the coupling to a line defect can be modelled by framed quivers. The associated spectral problem characterises the line defect completely. Read More

It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of giving a better understanding of the above conjecture, in this paper we revisit the description of framed BPS states of four-dimensional relativistic quantum field theories with eight conserved supercharges in terms of supersymmetric quantum mechanics. We unveil aspects of the deep interrelationship in between the Seiberg-dualities of the latter, the discrete symmetries of the theory in the bulk, and quantum discrete integrable systems. Read More

We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. Read More

BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper we approach this problem from the perspective of persistent homology. Read More

In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally compactified heterotic string theory, graded by electric and magnetic charges. The regularization is achieved by viewing the weighted sums of degeneracies as sums over charge excitations in the near-horizon attractor geometry of an arbitrarily chosen black hole background, and eliminating the unstable modes. Read More

We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions. Read More

The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line defect opens up a new BPS sector: framed BPS states can be bound to the defect. Read More

Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions. These defects are associated with divisors and are defined by prescribing certain boundary conditions for the gauge fields. Read More

We survey some features of equivariant instanton partition functions of topological gauge theories on four and six dimensional toric Kahler varieties, and their geometric and algebraic counterparts in the enumerative problem of counting holomorphic curves. We discuss the relations of instanton counting to representations of affine Lie algebras in the four-dimensional case, and to Donaldson-Thomas theory for ideal sheaves on Calabi-Yau threefolds. For resolutions of toric singularities, an algebraic structure induced by a quiver determines the instanton moduli space through the McKay correspondence and its generalizations. Read More

Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative N=2 gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated to the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. Read More

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. Read More

We study the relationship between the statistical mechanics of crystal melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric surfaces. We argue that, in contrast to their six-dimensional cousins, the two problems are related but not identical. We develop a vertex formalism for the crystal partition function, which calculates a generating function for the dimension 0 and 1 subschemes of the toric surface, and describe the modifications required to obtain the corresponding gauge theory partition function. Read More

We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is conjecturally equivalent to Donaldson-Thomas theory. We evaluate the partition function of the U(N) theory in its Coulomb branch on flat space by employing equivariant localization techniques on its noncommutative deformation. Read More

We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. Read More

We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kaehler parameters, one of which corresponds to the expected fibration over the sphere. Read More

We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. Read More

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Read More

We study effective gravitational F-terms, obtained by integrating an $U(N)$ adjoint chiral superfield $\Phi$ coupled to the ${\cal N}=1$ gauge chiral superfield $W_\alpha$ and supergravity, to arbitrary orders in the gravitational background. The latter includes in addition to the ${\cal N}=1$ Weyl superfield $G_{\alpha\beta\gamma}$, the self-dual graviphoton field strength $F_{\alpha\beta}$ of the parent, broken ${\cal N}=2$ theory. We first study the chiral ring relations resulting from the above non-standard gravitational background and find agreement, for gauge invariant operators, with those obtained from the dual closed string side via Bianchi identities for ${\cal N}=2$ supergravity coupled to vector multiplets. Read More