On Partition Functions of Hyperbolic Three-Geometry and Associated Hilbert Schemes

A. A. Bytsenko () and E. Elizalde ()
Additional contact information
A. A. Bytsenko: Universidade Estadual de Londrina, Caixa, Departamento de Física
E. Elizalde: Campus UAB, Facultat de Ciències, Consejo Superior de Investigaciones Científicas (ICE/CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC)

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 131-148 from Springer

Abstract: Abstract Highest-weight representations of infinite-dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions (elliptic genera) are conveniently transformed into product expressions, which may inherit the homology properties of appropriate (poly)graded Lie algebras. Specifically, the role of (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of partition functions and associated q-series is discussed. Examples of these connections in quantum field theory are considered (in particular, within the AdS/CFT correspondence), as the AdS3 case where one has Ruelle/Selberg spectral functions, whereas on the CFT side, partition functions and modular forms arise. These objects are here shown to have a common background, expressible in terms of Euler-Poincaré and Macdonald identities, which, in turn, describe homological aspects of (finite or infinite) Lie algebra representations. Finally, some other applications of modular forms and spectral functions (mainly related with the congruence subgroup of $$SL(2, \mathbb{Z})$$ ) to partition functions, Hilbert schemes of points, and symmetric products are investigated by means of homological and K-theory methods.

Keywords: Partition Function; Spectral Function; Zeta Function; Modular Form; Clifford Algebra (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_5

Ordering information: This item can be ordered from
http://www.springer.com/9781493902583

DOI: 10.1007/978-1-4939-0258-3_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().