TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics

Abstract

We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ${\mathbb{Z}}_4$-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two $D_3$-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian.

arXiv comment31 pages, 1 figure; Published version

References in corpus (37)

• Instantons and recursion relations in N=2 Susy gauge theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• The ODE/IM Correspondence
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Excited states by analytic continuation of TBA equations
• Y-system for Scattering Amplitudes
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• T-systems and Y-systems in integrable systems
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations
• On the Relation Between the Holomorphic Prepotential and the Quantum Moduli in SUSY Gauge Theories
• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• N-fold Supersymmetry in Quantum Mechanics - General Formalism -
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• TBA equations and resurgent Quantum Mechanics
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
• Instantons in Quantum Mechanics and Resurgent Expansions
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Holomorphic Anomaly and Quantum Mechanics
• RG-Whitham dynamics and complex Hamiltonian systems
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• TBA Equations and Quantization Conditions
• TBA equations for the Schrödinger equation with a regular singularity
• Y-System and Deformed Thermodynamic Bethe Ansatz
• Quantum Seiberg-Witten curve and Universality in Argyres-Douglas theories
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• $1/\epsilon$ problem in resurgence
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
• Notes on Wall Crossing and Instanton in Compactified Gauge Theory with Matter

Cited by in corpus (8)

• TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
• Thermodynamic Bethe ansatz and wall crossing for deformed supersymmetric quantum mechanics
• TBA equations and quantum periods for D-type Argyres-Douglas theories
• Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method
• Exact WKB in all sectors I: Potentials with degenerate saddles
• Exact-WKB Analysis of Two-level Floquet Systems
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Exact WKB in all sectors II: Potentials with non-degenerate saddles