arXiv subjects

Alessandro Tanzini

Publications and source records attributed to Alessandro Tanzini.

At least 73 records · Page 4Linked to original sources

arXiv2008

Topological branes, p-algebras and generalized Nahm equations

Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory

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arXiv2008

Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry

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.

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arXiv2007

The holomorphic anomaly for open string moduli

We complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.

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arXiv2007

Computing Amplitudes in topological M-theory

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.

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arXiv2006

Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory

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.

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arXiv2005

On topological M-theory

We construct a gauge fixed action for topological membranes on $G_2$-manifold 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. Moreover on $M\times S^1$ the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on $G_2$-manifolds. We also generalize our construction to topological $p$--branes on special manifolds by exploring a relation between vector cross product structures and TFTs.

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arXiv2005

Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds

We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT's (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.

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arXiv2004

The 3-string vertex and the AdS/CFT duality in the PP-wave limit

We pursue the study of string interactions in the PP-wave background and show that the proposal of hep-th/0211188 can be extended to a full supersymmetric vertex. Then we compute some string amplitudes in both the bosonic and fermionic sector, finding agreement with the field theory results at leading order in lambda'.

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arXiv2004

A note on string interaction on the pp-wave background

We consider type IIB string interaction on the maximally supersymmetric pp-wave background and discuss how the bosonic symmetries of the background are realized. This analysis shows that there are some interesting differences with respect to the flat-space case and suggests modifications to the existing form of the string vertex. We focus on the zero-mode part which is responsible for some puzzling string predictions about the N=4 SYM side. We show that these puzzles disappear when a symmetry preserving string interaction is used.

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arXiv2004

The Duality between IIB String Theory on PP-wave and N=4 SYM: a Status Report

The aim of this report is to give an overview of the duality between type IIB string theory on the maximally supersymmetric PP-wave and the BMN sector of N=4 Super Yang-Mills theory. The general features of the string and the field theory descriptions are reviewed, but the main focus of this report is on the comparison between the two sides of the duality. In particular, it is first explained how free IIB strings emerge on the gauge theory side and then the generalizations of this relation to the full interacting theory are considered. An ``historical'' approach is taken and the various proposals presented in the literature are described.

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arXiv2003

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.

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arXiv2003

Supergravity and the Knitting of the Kalb--Ramond Two-Form in Eight-Dimensional Topological Gravity

Topological euclidean gravity is built in eight dimensions for manifolds with $Spin(7) \subset SO(8)$ holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb--Ramond two-form gauge field. We then recover the complete $N=1, D=8$ supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.

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arXiv2002

String interactions and discrete symmetries of the pp-wave background

Free string theory on the plane-wave background displays a discrete Z2 symmetry exchanging the two transverse SO(4) rotation groups. This symmetry should be respected also at the interacting level. We show that the zero mode structure proposed in hep-th/0208148 can be completed to a full kinematical vertex, contrary to claims appeared in the previous literature. We also comment on the relation with recent works on the string-bit formalism and on the comparison with the field theory side of the correspondence.

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arXiv2002

Eight-Dimensional Topological Gravity and its Correspondence with Supergravity

A topological theory for euclidean gravity in eight dimensions is built by enforcing octonionic self-duality conditions on the spin connection. The eight-dimensional manifold must be of a special type, with G_2 or Spin(7) holonomy. The resulting theory is related to a twisted version of N=1, D=8 supergravity. The situation is comparable to that of the topological Yang--Mills theory in eight dimensions, for which the SO(8) invariance is broken down to Spin(7), but is recovered after untwisting the topological theory.

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arXiv2002

D-instantons on orbifolds and gauge/gravity correspondence

D-instantons are used to probe the near-horizon geometry of D3-branes systems on orbifold spaces. For fractional D3-branes, D-instanton calculus correctly reproduces the gauge beta-function and U(1)_R anomaly of the corresponding N=2 non-conformal Super Yang-Mills theories. For D3-branes wrapping the orbifold singularity, D-instantons can be identified with gauge instantons on ALE space, providing evidence of AdS/CFT duality for gauge theories on curved spaces.

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arXiv2002

Topological Gravity versus Supergravity on Manifolds with Special Holonomy

We construct a topological theory for euclidean gravity in four dimensions, by enforcing self-duality conditions on the spin connection. The corresponding topological symmetry is associated to the SU(2) X diffeomorphism X U(1) invariance. The action of this theory is that of d=4, N=2 supergravity, up to a twist. The topological field theory is SU(2) invariant, but the full SO(4) invariance is recovered after untwist. This suggest that the topological gravity is relevant for manifolds with special holonomy. The situation is comparable to that of the topological Yang-Mills theory in eight dimensions, for which the SO(8) invariance is broken down to Spin(7), but is recovered after untwisting the topological theory.

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arXiv2001

D-instanton probes of N=2 non-conformal geometries

D-instanton calculus has proved to be able to probe the AdS near horizon geometry for $N$ D-branes systems which, when decoupled from gravity, yield four dimensional superconformal gauge theories with various matter content. In this work we extend previous analysis to encompass fractional brane models which give rise to non conformal N=2 Super Yang-Mills theories. Via D-instanton calculus we study the geometry of such models for finite $N$ and recover the $β$ function of the gauge coupling constants which is expected in non conformal gauge theories. We also give a topological matrix theory formulation for the D-instanton action of these theories. Finally, we revisit the related system where the D3-branes wrap a ${\real}^4/{\zet}_p$ orbifold singularity and the D(-1) branes are associated to instanton solutions of four-dimensional gauge theories in the blown down ALE space.

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arXiv2000

On the Multi-Instanton Measure for Super Yang--Mills Theories

In this paper we revisit the arguments that have led to the proposal of a multi-instanton measure for supersymmetric Yang-Mills theories. We then recall how the moduli space of gauge connections on $\real^4$ can be built from a hyperkähler quotient construction which we generalize to supermanifolds. The measure we are looking for is given by the supermetric of the supermoduli space thus introduced. To elucidate the construction we carry out explicit computations in the case of N=2 supersymmetric Yang-Mills theories.

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