Making use of the exact solutions of the N = 2 supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional N = 2 SCFTs.

We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N = 1 super Yang-Mills theory with chiral and antichiral superfields, which has N = 1 2 supersymmetry on the noncommutative superspace. We also construct the action of N = 2 super Yang-Mills theory. It is shown that this theory has only N = 1 2 supersymmetry.

We derive a system of TBA equations governing the exact WKB periods in onedimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. Our derivation builds upon the solution of similar Riemann-Hilbert problems in the study of BPS spectra in N = 2 gauge theories and of minimal surfaces in AdS. We also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of PT-symmetric cubic oscillators and quartic oscillators. arXiv:1811.04812v3 [hep-th] 31 Jan 2019Contents -1 -periods involved in the problem. However, this flourishing of ideas did not provide alternative computational methods in Quantum Mechanics. One was supposed to calculate the WKB series and their Borel resummations with traditional tools.Partially inspired by the results of [3], a correspondence between certain quantum mechanical models in one dimension and integrable models (or ODE/IM correspondence) was proposed by Dorey and Tateo in [7]. This correspondence was originally based on functional relations discovered in the context of resurgent Quantum Mechanics, which are similar to Baxter-type equations appearing in integrable systems. The ODE/IM correspondence makes it possible to write down TBA equations which calculate efficiently and exactly some of the quantities appearing in the quantum mechanical models, like spectral determinants and Borel resummations of WKB periods. An important limitation of the ODE/IM correspondence is that it applies to very special quantum-mechanical models, namely, monic potentials of the form V (x) = x M (and a limited amount of perturbations thereof).In this paper we will present TBA equations governing the WKB periods for general polynomial potentials in one dimension, providing in this way a generalization of the ODE/IM correspondence. The basic idea was already pointed out by Voros in his seminal paper [3], where he called it the "analytic bootstrap" for the exact WKB method. In this approach, the fundamental objects are the WKB periods, which are (Borel resummed) perturbative series in the Planck constant. These periods can be characterized by two types of data: their classical limit and their discontinuity structure, which has been known since the work of [3,4,6]. In the theory of resurgence, this discontinuity structure is encoded in the action of the so-called Stokes automorphisms. As Voros explained, we can think about these data as defining a Riemann-Hilbert problem. Building on recent developments in seemingly very different contexts [8][9][10][11][12][13][14][15], we show that Voros' Riemann-Hilbert problem has a solution in terms of a TBA-like system, which determines the exact dependence of the WKB periods on the Planck constant 1 . The TBA system of [7] is recove...

We study classical open string solutions with a null polygonal boundary in AdS 3 in relation to gluon scattering amplitudes in N = 4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS n and generalized parafermions.

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling which correspond to minimal surfaces with a light-like polygonal boundary in AdS_3. We find a concise expression of the remainder function in terms of the T-function of the associated thermodynamic Bethe ansatz (TBA) system. Continuing our previous work on the analytic expansion around the CFT/regular-polygonal limit, we derive a formula of the leading-order expansion for the general 2n-point remainder function. The T-system allows us to encode its momentum dependence in only one function of the TBA mass parameters, which is obtained by conformal perturbation theory. We compute its explicit form in the single mass cases. We also find that the rescaled remainder functions at strong coupling and at two loops are close to each other, and their ratio at the leading order approaches a constant near 0.9 for large n.Comment: 36 pages, 5 figures, v2: published version, v3: minor correction

We study gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS 3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T-and Yfunctions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the relation between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T-and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.for the Y-functions from the g-functions and determine the analytic form of the remainder function near the CFT point.In this paper, we study the remainder function for 2ñ-point gluon scattering amplitudes at strong coupling, which correspond to minimal surfaces in AdS 3 with a 2ñ-gonal light-like boundary. This corresponds to the case where the gluon momenta are in R 1,1 . In [9] the related integrable system was shown to be the homogeneous sine-Gordon model (HSG) [17] with purely imaginary resonance parameters. The relevant CFT is the generalized parafermions SU(ñ − 2) 2 /U(1)ñ −2 [18]. In this paper we will study the boundary and bulk perturbation of the generalized parafermions and calculate the ratios of the g-functions. For the octagon (ñ = 4) and the decagon (ñ = 5), we will calculate the perturbative corrections to the T-/Y-functions, the free energy and the remainder function explicitly. We compare these analytic expressions of the remainder function with the 2-loop formulas proposed in [19][20][21] around the CFT limit.The above analytic results are important to understand the structure and the momentum dependence of the amplitudes at strong coupling exactly. The purpose of this paper is to take a step toward this direction by analyzing the TBA system near the CFT point from the conformal perturbation theory (CPT). A point in our discussion is that not only the free energy but also the Y-functions can be discussed in this framework owing to the relation between the T-/Y-functions and the g-functions.This paper is organized as follows. In section 2, we review the TBA system for the minimal surfaces in AdS 3 . In section 3, we discuss the HSG model and the free energy for the integrable bulk perturbations. In section 4, we study the HSG model from the CPT of the generalized parafermions and the relation between the Tfunctions and the g-functions. In section 5, we investigate the small mass expansions of the g-function and the remainder function for the octagon. In section 6, we argue the corrections to the free energy, the T-/Y-fu...

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p, q) fivebranes and (p, q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p, q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.

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