Back to Search
Start Over
T, Q and periods in SU(3) $$ \mathcal{N} $$ = 2 SYM
- Source :
- Journal of High Energy Physics, Journal of High Energy Physics, Vol 2020, Iss 3, Pp 1-21 (2020)
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- We consider the third order differential equation derived from the deformed Seiberg-Witten differential for pure $$ \mathcal{N} $$ N = 2 SYM with gauge group SU(3) in Nekrasov- Shatashvili limit of Ω-background. We show that this is the same differential equation that emerges in the context of Ordinary Differential Equation/Integrable Models (ODE/IM) correspondence for 2d A2 Toda CFT with central charge c = 98. We derive the corresponding QQ and related T Q functional relations and establish the asymptotic behaviour of Q and T functions at small instanton parameter q → 0. Moreover, numerical integration of the Floquet monodromy matrix of the differential equation leads to evaluation of the A-cycles a1,2,3 at any point of the moduli space of vacua parametrized by the vector multiplet scalar VEVs (tr 𝜙2) and (tr 𝜙3) even for large values of q which are well beyond the reach of instanton calculus. The numerical results at small q are in excellent agreement with instanton calculation. We conjecture a very simple relation between Baxter’s T -function and A-cycle periods a1,2,3, which is an extension of Alexei Zamolodchikov’s conjecture about Mathieu equation.
- Subjects :
- Physics
Floquet theory
Nuclear and High Energy Physics
Instanton
Differential equation
Monodromy matrix
Conformal and W Symmetry
Supersymmetric Gauge Theory
High Energy Physics::Theory
symbols.namesake
Mathieu function
Nonperturbative Effects
Gauge group
Ordinary differential equation
symbols
Supersymmetry and Duality
lcsh:QC770-798
lcsh:Nuclear and particle physics. Atomic energy. Radioactivity
Multiplet
Mathematical physics
Subjects
Details
- ISSN :
- 10298479
- Volume :
- 2020
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....27f65b3b3fba25da1ddc463bd0b7eb27