Resurgence analysis of 2d Yang-Mills theory on a torus

Self Cite

We study the large N 't Hooft expansion of the chiral partition function of 2d U (N ) Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deformed partition function. We also study the behavior of the deformed partition function both in the strong coupling/large area limit and in the weak coupling/small area limit. In particular, we observe that drastic simplification occurs in the weak coupling/small area limit, giving another nontrivial support for our anti-holomorphic deformation.

Section: Small T Regimesupporting

confidence: 77%

“…Using this fact one can, in principle, compute F g up to any g from the above expression. Moreover, if we expand Z as Z = e F 1 (1 + ∞ n=1 g 2n s Z n ), Z n obeys a simple recursion relation, originally found in [25] and improved in [32], which determines F g much more efficiently than just expanding (2.5).…”

Section: )mentioning

confidence: 99%

Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited

Sakai

2019

Self Cite

“…The resurgence analysis applied to the torus partition function in Ref. [48] might be useful in this regard.…”

Section: Discussionmentioning

confidence: 99%

Entanglement entropy and the large N expansion of two-dimensional Yang-Mills theory

Donnelly

Timmerman

Valdés-Meller

2020

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large N . We calculate entanglement entropy in the 1/N expansion by mapping the theory to a system of N fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the "Boltzmann entropy", log dim(R) per point of the entangling surface, which counts the number of distinct microstates, and the "Shannon entropy", − p R log p R , which captures fluctuations of the macroscopic state. We find that the entropy scales as N 2 in the large N limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with N , and confirm this behaviour with numerical simulations. While the term of order N is surprising from the point of view of the string dual -in which only even powers of N appear in the partition function -we trace it to a breakdown of large N counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.

“…The conjecture states that the Borel singularity corresponding to the bion could become the renormalon singularity at −2S I /β 0 due to renormalization or decompactification. In spite of the recent progress on compactified CP N −1 models with twisted boundary conditions [103][104][105][106][107] and the intensive studies on the resurgence in the 2D models [108][109][110][111][112][113][114][115][116][117][118][119][120][121][122], the conjecture has not yet been verified even in the 2D sigma models.…”

Section: Introductionmentioning

confidence: 99%

Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models

Fujimori

Kamata

Misumi

et al. 2019

We derive the semiclassical contributions from the real and complex bions in the twodimensional CP N −1 sigma model on R × S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the CP N −1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find that the non-perturbative contribution vanishes in the supersymmetric case and it has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity in non-supersymmetric cases. This is the first explicit result indicating the relation between the complex bion and the infrared renormalon. * Electronic address: toshiaki.fujimori018(at)