Refined Chern–Simons versus Vogel universality

Krefl, Daniel; Schwarz, Albert

doi:10.1016/j.geomphys.2013.08.002

Cited by 21 publications

(37 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…include the usual Chern-Simons theories, but, after some extension of range of parameters, as well the refined versions thereof, as shown in [13].…”

Section: Jhep10(2015)045mentioning

confidence: 99%

“…The normalization mentioned is called minimal one and is defined by the only negative Vogel parameter (usually v 1 below) to be equal to −2. As discovered in [13], (2.1) also includes the refined Chern-Simons theories of [7,9] at appropriate values of parameters, though Vogel's condition will not be satisfied anymore in the refined case. It is convenient to rewrite F as follows.…”

Section: Generalitiesmentioning

confidence: 99%

See 1 more Smart Citation

Exact Chern-Simons / Topological String duality

Krefl

Mkrtchyan

2015

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Abstract:We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N . In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extended to refined Chern-Simons with orthogonal groups.

show abstract

“…include the usual Chern-Simons theories, but, after some extension of range of parameters, as well the refined versions thereof, as shown in [13].…”

Section: Jhep10(2015)045mentioning

confidence: 99%

Section: Generalitiesmentioning

confidence: 99%

Exact Chern-Simons / Topological String duality

Krefl

Mkrtchyan

2015

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Relation (4.8) implies that we have sort of a special geometry relation 20) up to some integration constant c (more precisely function). As E and A possess an expansion in ξ, so does F SG (N ), i.e.,…”

Section: Free Energymentioning

confidence: 99%

“…The period a D is the preferred flat coordinate near the strongly coupled regime. The regular part, F reg , can for instance be inferred via analytic continuation from weak coupling, making use of the underlying special geometry and holomorphic anomaly equations (originating from modularity of the partition function) [31,42],…”

Section: Strong Couplingmentioning

confidence: 99%

See 1 more Smart Citation

Non-perturbative quantum geometry II

Krefl

2014

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The Nekrasov-Shatashvili limit of β-ensembles with polynomial potential and N = 2 supersymmetric gauge theories in the Ω-background is intimately related to complex one-dimensional quantum mechanics. Multi-instanton corrections in quantum mechanics, inferable from exact quantization conditions, imply additional non-perturbative corrections to the Nekrasov-Shatashvili free energies. Besides filling some of the gaps in previous derivations, we present analytic expressions for such additional non-perturbative corrections in the case of SU(2) gauge theory expanded at strong coupling. In contrast, at weak coupling these additional non-perturbative corrections appear to be negligible.

show abstract

Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

2016

View full text Add to dashboard Cite

We derive the analog of the large N Gross-Taylor holomorphic string expansion for the refinement of q-deformed U(N) Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit q = 1, the expansion defines a new β-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β-ensembles of matrix models arising in refined topological string theory.

show abstract

Refined Chern–Simons versus Vogel universality

Abstract: We study the relation between the partition function of refined SU(N) and SO(2N)

Cited by 21 publications

References 26 publications

Exact Chern-Simons / Topological String duality

Exact Chern-Simons / Topological String duality

Non-perturbative quantum geometry II

Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

Contact Info

Product

Resources

About