Check-Operators and Quantum Spectral Curves

Abstract

We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model

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Cited by in corpus (9)

• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Sum rules for characters from character-preservation property of matrix models
• Cut and join operator ring in Aristotelian tensor model
• A slow review of the AGT correspondence
• Orthogonal Polynomials in Mathematical Physics
• Twin Peaks: A possible signal in the production of resonances beyond special relativity