Shota Komatsu

Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem

A bstractWe consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the flow-time defined at a certain asymptotic region close to the critical point, and it is generated by solving the gradient flow equation downward. The associated complete set of tangent vectors is also generated in the same manner. Molecular dynamics is then formulated as a constrained dynamical system, where the equations of motion with Lagrange multipliers are solved by the second-order constraint-preserving symmetric integrator. The algorithm is tested in the λϕ4 model at finite density, by choosing the thimbles associated with the classical vacua for subcritical and supercritical values of chemical potential. For the lattice size L = 4, we find that the residual sign factors average to not less than 0.99 and are safely included by reweighting and that the results of the number density are consistent with those obtained by the complex Langevin simulations.

On holographic three point functions for GKP strings from integrability

A bstractAdapting the powerful integrability-based formalism invented previously for the calculation of gluon scattering amplitudes at strong coupling, we develop a method for computing the holographic three point functions for the large spin limit of GubserKlebanov-Polyakov (GKP) strings. Although many of the ideas from the gluon scattering problem can be transplanted with minor modifications, the fact that the information of the external states is now encoded in the singularities at the vertex insertion points necessitates several new techniques. Notably, we develop a new generalized Riemann bilinear identity, which allows one to express the area integral in terms of appropriate contour integrals in the presence of such singularities. We also give some general discussions on how semiclassical vertex operators for heavy string states should be constructed systematically from the solutions of the Hamilton-Jacobi equation.

Wave functions and correlation functions for GKP strings from integrability

A bstractWe develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in AdS3 spacetime, left unevaluated in our previous work [arXiv:1110.3949] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.

Three-point functions in the SU(2) sector at strong coupling

A bstractExtending the methods developed in our previous works (arXiv:1110.3949, arXiv:1205.6060), we compute the three-point functions at strong coupling of the non-BPS states with large quantum numbers corresponding to the composite operators belonging to the so-called SU(2) sector in the

Hexagonalization of correlation functions

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Novel construction and the monodromy relation for three-point functions at weak coupling

= 4 super-Yang-Mills theory in four dimensions. This is achieved by the semi-classical evaluation of the three-point functions in the dual string theory in the AdS3× S3 spacetime, using the general one-cut finite gap solutions as the external states. In spite of the complexity of the contributions from various parts in the intermediate stages, the final answer for the three-point function takes a remarkably simple form, exhibiting the structure reminiscent of the one obtained at weak coupling. In particular, in the Frolov-Tseytlin limit the result is expressed in terms of markedly similar integrals, however with different contours of integration. We discuss a natural mechanism for introducing additional singularities on the worldsheet without affecting the infinite number of conserved charges, which can modify the contours of integration.

Structure constants at wrapping order

A bstractWe propose a nonperturbative framework to study general correlation functions of single-trace operators in N

The hexagon in the mirror: the three-point function in the SoV representation

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