Sphere partition functions and the Zamolodchikov metric

By Efrat Gerchkovitz, Joaquim Gomis, Z. Komargodski. 2014

178 citations recorded by the source corpus.

A bstractWe study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In odd dimensions, this quantity is physical and independent of the exactly marginal couplings. In even dimensions, this object is generally regularization scheme dependent and thus unphysical. However, in the presence of additional symmetries, the partition function of even-dimensional CFTs can become physical. For two-dimensional N=22$$ \mathcal{N}=\left(2,2\right) $$ supersymmetric CFTs, the continuum partition function exists and computes the Kähler potential on the chiral and twisted chiral superconformal manifolds. We provide a new elementary proof of this result using Ward identities on the sphere. The Kähler transformation ambiguity is identified with a local term in the corresponding N=22$$ \mathcal{N}=\left(2,2\right) $$ supergravity theory. We derive an analogous, new, result in the case of four-dimensional N=2$$ \mathcal{N}=2 $$ supersymmetric CFTs: the S4 partition function computes the Kähler potential on the superconformal manifold. Finally, we show that N=1$$ \mathcal{N}=1 $$ supersymmetry in four dimensions and N=11$$ \mathcal{N}=\left(1,1\right) $$ supersymmetry in two dimensions are not sufficient to make the corresponding sphere partition functions well-defined functions of the exactly marginal parameters.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f6b2f3e9380e703d47dfa85742dd075d2137b2f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. H. Casini
3. T. Takayanagi
4. M. Huerta
5. Silviu S. Pufu
6. A. Yale
7. Z. Komargodski
8. T. Nishioka

In Nuclear and High Energy Physics

1. R. Myers
2. Silviu S. Pufu
3. T. Takayanagi
4. H. Casini
5. M. Huerta
6. Z. Komargodski
7. A. Yale
8. David Simmons-Duffin

In Statistical and Nonlinear Physics

1. R. Myers
2. Silviu S. Pufu
3. H. Casini
4. M. Huerta
5. A. Yale
6. Z. Komargodski
7. T. Takayanagi
8. B. C. Rees

Citations in the corpus

• $$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, background): “ect to ˝ s (5.8).25 It would be interesting to derive these dierential m= 0, the S4 free energy simply captures the Kahler potential on the conformal manifold of the N= 4 SYM which is rather trivial [83]. 25Such dierential equations for the higher derivative couplings R4 and D4 4 are a consequence o”
• Correlation functions of Coulomb branch operators (2016, methodology): “Indeed, if we add to the action of the SCFT on S(4) the (16)We change the normalization of the deformation by a factor of 1/32 with respect to [5, 6] in order to make formulae below simpler.”
• The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, methodology): “In many N = 2 SCFTs, this OPE coefficient is made accessible by the relation between the Kähler metric on the conformal manifold and the S4 partition function [123],”
• Mutual information and the F-theorem (2015, background): “See also [41, 42] for discussion from the perspective of the free energy.”