We study the quantum Seiberg-Witten (SW) curves for (A 1 , G)-type Argyres-Douglas (AD) theory by taking the scaling limit of the quantum SW curve of N = 2 gauge theory with gauge group G. For G = A r , the quantum SW curve of the AD theory is consistent with the scaling limit of the curve of the gauge theory. For G = D r , we need the quantum correction to the SW curve of the AD theory, which depends on the quantization condition of the original SW curve. We also study the universality of the quantum SW curves for (A 1 , A 3 ) and (A 1 , D 4 )-type AD theories.

We study the quantum Seiberg-Witten periods of N = 2 superconformal field theories which are obtained by taking the scaling limit of N = 2 SU (N c ) SQCD around the superconformal fixed point. The quantum Seiberg-Witten curves of these superconformal field theories are shown to be classified into the Schrödinger type and the SQCD type, which depend on flavor symmetry at the fixed point. We study the quantum periods and compute the differential operators which relate the quantum periods to the classical ones up to the fourth-order in the deformation parameter. IntroductionThe low-energy description of N = 2 supersymmetric gauge theories has singularities in the strong coupling region [1,2]. In particular, there appears an IR fixed point at a locus of the Coulomb branch, where mutually non-local BPS particles become massless [3,4,5].The dynamics around the fixed point is described by an interacting N = 2 superconformal field theory called the Argyres-Douglas (AD) theory.One can study the BPS spectrum of the AD theory from the Seiberg-Witten (SW) curve, which is obtained by degeneration of the SW curve of the UV gauge theory. It is also realized from the compactification of the six-dimensional N = (2, 0) superconformal field theory on a punctured Riemann surface [6,7,8] and classified in [9,10,11,12].One can also study the SW theories in the Nekrasov-Shatashvili (NS) limit of the Omega-background [13]. The Omega background deforms four dimensional spacetime by the two-dimensional torus action [14]. The NS limit is defined by the limit where one of the deformation parameters goes to zero. In this limit, the deformed theory is reformulated by the quantum SW curve [15], which is a differential equation obtained by the quantization of the symplectic structure based on the SW differential. The deformation parameter plays a role of the Planck constant.The WKB analysis of the quantum SW curve determines the deformed SW periods [16,17,18]. In the weak coupling region, the quantum corrections to the SW periods agree with those obtained from the NS limit of the Nekrasov partition function [15,19,20,21].In the strong coupling region such as the massless monopole/dyon point, the quantum SW periods for the SU(2) SQCD with N f ≤ 4 have been studied in [22,23,24]. The relation to the topological strings have been studied in [25,26]. (See also [27,28,29,30] for its relation to CFT.)In the previous papers [31,32], we have studied the quantum SW curves for the AD theories associated with N = 2 SU(2) SQCD, the (A 1 , A r )-type and (A 1 , D r )-type AD theories. We have calculated the quantum corrections to the SW periods up to the fourth order in the deformation parameter and confirmed that they are consistent with the scaling limit of the quantum periods of the UV theories. Recently the exact WKB periods for the quantum SW curve of (A 1 , A r )-type AD theory are shown to be determined by the

We consider massless Majorana fermion systems with G = Z N , SO(N ), and O(N ) symmetry in one-dimensional spacetime. In these theories, phase ambiguities of the partition functions are given as the exponential of the η-invariant of the Dirac operators in two dimensions, which is a bordism invariant. We construct sufficient numbers of bordism invariants to detect all bordism classes. Then, we classify global anomalies by calculating the η-invariant of these bordism classes.

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