TWO-SPHERE PARTITION FUNCTIONS AND K¨AHLER POTENTIALS ON CY MODULI SPACES

2018 ◽  
Vol 108 (9-10) ◽  
pp. 725-725
Author(s):  
K. ALESHKIN ◽  
A. BELAVIN ◽  
A. LITVINOV
Keyword(s):  
Moduli Spaces ◽  
Partition Functions

scholarly journals Counting curves on surfaces

2017 ◽  
Vol 28 (02) ◽  
pp. 1750012
Author(s):  
Norman Do ◽  
Musashi A. Koyama ◽  
Daniel V. Mathews
Keyword(s):  
Moduli Spaces ◽  
Symplectic Geometry ◽  
Differential Forms ◽  
Combinatorial Problem ◽  
Partition Functions ◽  
Low Dimensional Topology ◽  
Moduli Spaces Of Curves ◽  
Finite Set ◽  
Curves On Surfaces ◽  
Low Dimensional

We consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology: for a compact surface [Formula: see text], with a finite set of points [Formula: see text] fixed on its boundary, how many configurations of disjoint arcs are there on [Formula: see text] whose boundary is [Formula: see text]? We find that this enumerative problem, counting curves on surfaces, has a rich structure. We show that such curve counts obey an effective recursion, in the general spirit of topological recursion, and exhibit quasi-polynomial behavior. This “elementary curve-counting” is in fact related to a more advanced notion of “curve-counting” from algebraic geometry or symplectic geometry. The asymptotics of this enumerative problem are closely related to the asymptotics of volumes of moduli spaces of curves, and the quasi-polynomials governing the enumerative problem encode intersection numbers on moduli spaces. Among several other results, we show that generating functions and differential forms for these curve counts exhibit structure that is reminiscent of the mathematical physics of free energies, partition functions and quantum curves.

scholarly journals The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

1997 ◽  
Vol 12 (06) ◽  
pp. 381-392 ◽  
Author(s):  
Mitsuko Abe
Keyword(s):  
Partition Function ◽  
Gravity Model ◽  
Moduli Spaces ◽  
Partition Functions ◽  
K3 Surface ◽  
Analytic Manifold ◽  
Rham Complex ◽  
De Rham ◽  
Complex Analytic Manifold ◽  
Equivalent Class

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some [Formula: see text]-torsions. [Formula: see text]-torsion is the extension of R-torsion for the de Rham complex to that for the [Formula: see text]-complex of a complex analytic manifold.

scholarly journals Instantons and vortices on noncommutative toric varieties

2014 ◽  
Vol 26 (09) ◽  
pp. 1430008 ◽  
Author(s):  
Lucio S. Cirio ◽  
Giovanni Landi ◽  
Richard J. Szabo
Keyword(s):  
Moduli Spaces ◽  
Toric Varieties ◽  
Partition Functions ◽  
Toric Geometry ◽  
Monoidal Categories ◽  
Klein Quadric ◽  
Noncommutative Algebraic Geometry ◽  
Fundamental Matter ◽  
Braided Monoidal Categories ◽  
Noncommutative Gauge Theories

We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.

scholarly journals Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Arash Arabi Ardehali ◽  
Junho Hong
Keyword(s):  
Partition Function ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Asymptotic Expression ◽  
Effective Field ◽  
Asymptotic Result ◽  
Partition Functions ◽  
Abelian Gauge ◽  
Scale Hierarchy

Abstract We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

scholarly journals Topological strings on toric geometries in the presence of Lagrangian branes

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
M. Nouman Muteeb
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Topological Strings ◽  
Moduli Spaces ◽  
Topological String ◽  
Lagrangian Submanifolds ◽  
Partition Functions ◽  
Special Lagrangian ◽  
Special Lagrangian Submanifolds ◽  
Mass Deformation

AbstractWe propose expressions for refined open topological string partition function on certain non-compact Calabi Yau 3-folds with topological branes wrapped on the special lagrangian submanifolds. The corresponding web diagrams are partially compact and a lagrangian brane is inserted on one of the external legs. Partial compactification introduces a mass deformation in the corresponding gauge theory. We propose conjectures that equate these open topological string partition functions with the generating function of equivaraint indices on certain quiver moduli spaces. To obtain these conjectures we use the identification of topological string partition functions with equivariant indices on the instanton moduli spaces.

Two-Sphere Partition Functions and Kähler Potentials on CY Moduli Spaces

JETP Letters ◽  
2018 ◽  
Vol 108 (10) ◽  
pp. 710-713 ◽  
Author(s):  
K. Aleshkin ◽  
A. Belavin ◽  
A. Litvinov
Keyword(s):  
Moduli Spaces ◽  
Partition Functions

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

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