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Register a new userQuasi-local formulation of the mirror TBA
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We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are connected by the TBA equations are at most next to nearest neighbors with respect to the Y-system diagram of AdS/CFT.
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We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.
By considering the continuum scaling limit of the $A_{4}$ RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter $xi $ which plays the role of the perturbing boundary field $phi_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $mathcal{B}_{(1,2)}to mathcal{B}_{(2,1)}$ example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix.
The integrals of motion of the tricritical Ising model are obtained by Thermodynamic Bethe Ansatz (TBA) equations derived from the A_4 integrable lattice model. They are compared with those given by the conformal field theory leading to a unique one-to-one lattice-conformal correspondence. They can also be followed along the renormalization group flows generated by the action of the boundary field phi_{1,3} on conformal boundary conditions in close analogy to the usual TBA description of energies.
A definition of quasi-local energy in a gravitational field based upon its embedding into flat space is discussed. The outcome is not satisfactory from many points of view.
Torsion gravity is a natural extension to Einstein gravity in the presence of the fermion matter sources. In this paper we adopt Walds covariant method of Noether charge to construct the quasi-local energy of the Einstein-Cartan-fermion system, and find that its explicit expression is formally independent of the coupling constant between torsion and axial current. This seemingly topological nature is unexpected and is reminiscent of similar nature of quantum Hall effect and topological insulator. However, the coupling dependence does enter when evaluating it on-shell, and thus the topological nature is pseudo. Based on the expression of the quasi-local energy, we evaluate it for a particular solution on the entanglement wedge and find the agreement with the holographic relative entropy obtained before. This shows that the equivalence of these two quantities in the Einstein-Cartan-fermion system. Moreover, the quasi-local energy in this case is not always positive definite so that it provides an example of swampland in torsion gravity. Based on the covariant Noether charge, we also derive the nonzero fermion effect on Komar angular momentum. The implication of our results to the tests of torsion gravity in the future gravitational wave astronomy is also discussed.
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