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We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS 2 background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N = 4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS 5 × S 5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2, 2|4) superalgebra, in particular of the type "Beauty" and "Beast".Non-abelian gauge theories discovered more than 40 years ago still do not have a satisfactory quantitative description at the intermediate and strong coupling regimes, in spite of their great importance for fundamental physics and substantial efforts of many theoretical and computational physicists and mathematicians. The most important of them, QCD and the standard model, are well studied perturbatively and to some extent we know the qualitative picture of strong coupling phenomena, such as confinement or instanton-induced processes. Nowadays lattice calculations provide some reasonable quantitative data confirming the qualitative picture, but they cannot replace systematic analytical methods, still absent.A new boost to the study of these questions was given by supersymmetry: Supersymmetric Yang-Mills (SYM) theories appeared to have special BPS sectors where certain physical quantities, protected from renormalization by supersymmetry, can be computed exactly. Outstanding examples are the Seiberg-Witten low-energy effective action in N = 2 SYM and the Dijkgraaf-Vafa effective potential in N = 1 SYM. This shed a good deal of light on the role of confinement and of the Higgs mechanism in strongly coupled supersymmetric gauge theories. Still, the BPS sector is only a tiny fraction of the theory, the rest being as difficult to access as in non-supersymmetric theories.New hope came from an issue which was not expected to play any role in interacting four-dimensional theories: Quantum integrability, discovered in a pioneering work of Hans Bethe [1] in relation to the Heisenberg XXX chain, usually applicable exclusively to exact solutions in (1+1)-dimensional theories, made its breakthrough into fourdimensional large-N c gauge theories. Here, the simplifications of large-N c lead to an essentially two-dimensional description of parts of the theory bypassing a no-go theorem for four dimensions. The first traces of integrability were observed and proved by Lipatov for reggeized gluons in QCD [2]. In [3] the equivalence of the reggeon Hamiltonian and the Hamiltonian of the Heisenberg XXX 0 spin chain was shown. This result was independently derived by Faddeev and Korchemsky in [4] where also the Bethe and Baxter equations for this model are analyzed.The observations of integrability look especially interesting and hopeful in the maximally supersymmetric gauge the...

We construct the general algebraic curve of degree four solving the classical sigma model on R × S 5 . Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N = 4 SYM, also constructed here. We explicitly reproduce some particular solutions.

We consider entanglement through permeable interfaces in the c = 1 (1+1)dimensional conformal field theory. We compute the partition functions with the interfaces inserted. By the replica trick, the entanglement entropy is obtained analytically.The entropy scales logarithmically with respect to the size of the system, similarly to the universal scaling of the ordinary entanglement entropy in (1+1)-dimensional conformal field theory. Its coefficient, however, is not constant but controlled by the permeability, the dependence on which is expressed through the dilogarithm function.The sub-leading term of the entropy counts the winding numbers, showing an analogy to the topological entanglement entropy which characterizes the topological order in (2+1)-dimensional systems.