65 research outputs found
ODE/IM correspondence and the Argyres-Douglas theory
We study the quantum spectral curve of the Argyres-Douglas theories in the
Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM
correspondence we investigate the quantum integrable model corresponding to the
quantum spectral curve. We show that the models for the -type theories
are non-unitary coset models at the
fractional level , which appear in the study of the 4d/2d
correspondence of superconformal field theories. Based on the WKB
analysis, we clarify the relation between the Y-functions and the quantum
periods and study the exact Bohr-Sommerfeld quantization condition for the
quantum periods. We also discuss the quantum spectral curves for the D and E
type theories.Comment: 28 pages, 1 figure. Typos corrected, a reference is added. Published
versio
T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
We first perform bosonic T-duality transformation on one of the marginal TsT
(T-duality, shift, T-duality)-deformed spacetime, which
corresponds to 4D non-commutative super Yang-Mills theory
(NCSYM). We then construct the solution to killing spinor equations of the
resulting background, and perform the fermionic T-duality transformation. The
final dual geometry becomes the usual but with the constant
NS-NS B-field depending on the non-commutative parameter. As applications, we
study the gluon scattering amplitude and open string (Wilson loop) solution in
the TsT-deformed spacetime, which are dual to the null
polygon Wilson loop and the folded string solution respectively in the final
dual geometry.Comment: 24 pages, latex, references added, published versio
ODE/IM correspondence for modified affine Toda field equation
We study the massive ODE/IM correspondence for modified affine
Toda field equation. Based on the -system for the solutions of the
associated linear problem, we obtain the Bethe ansatz equations. We also
discuss the T-Q relations, the T-system and the Y-system, which are shown to be
related to those of the integrable system. We consider the case
that the solution of the linear problem has a monodromy around the origin,
which imposes nontrivial boundary conditions for the T-/Y-system. The
high-temperature limit of the T- and Y-system and their monodromy dependence
are studied numerically.Comment: 1+21 pages, 2 figures, Typos correcte
TBA equations and resurgent Quantum Mechanics
We derive a system of TBA equations governing the exact WKB periods in
one-dimensional 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
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.Comment: 42 pages, Typos corrected, references are added, published versio
Limiting Behavior of Constraint Minimizers for Inhomogeneous Fractional Schr\"{o}dinger Equations
This paper is devoted to the -constraint variational problem
\begin{equation*}
We study -normalized solutions of the following inhomogeneous fractional
Schr\"{o}dinger equation \begin{equation*} (-\Delta)^{s}
u(x)+V(x)u(x)-a|x|^{-b}|u|^{2\beta^2}u(x)=\mu u(x)\ \ \mbox{in}\ \ \R^{N}.
\end{equation*} Here , , ,
, and is
an external potential. We get -normalized solutions of the above equation
by solving the associated constrained minimization problem. We prove that there
exists a critical value such that minimizers exist for , and
minimizers do not exist for any . In the case of , one can obtain
the classification results of the existence and non-existence for constraint
minimizers, which are depended strongly on the value of . For ,
the limiting behavior of nonnegative minimizers is also analyzed when tend
to from below
deformation of chiral bosons and Chern-Simons AdS gravity
We study the deformation of the chiral bosons and show the
equivalence between the chiral bosons of opposite chiralities and the scalar
fields at the Hamiltonian level under the deformation. We also derive the
deformed Lagrangian of more generic theories which contain an arbitrary number
of chiral bosons to all orders. By using these results, we derive the
deformed boundary action of the AdS gravity theory in the
Chern-Simons formulation. We compute the deformed one-loop torus partition
function, which satisfies the flow equation up to the one-loop
order. Finally, we calculate the deformed stress tensor of a solution
describing a BTZ black hole in the boundary theory, which coincides with the
boundary stress tensor derived from the BTZ black hole with a finite cutoff.Comment: 29 pages, references adde
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