High Energy Physics Theory

We study multi-boundary correlators of Witten-Kontsevich topological gravity in two dimensions. We present a method of computing an open string like expansion, which we call the 't Hooft expansion, of then-boundary correlator for anynup to any order by directly solving the KdV equation. We first explain how to compute the 't Hooft expansion of the one-boundary correlator. The algorithm is very similar to that for the genus expansion of the open free energy. We next show that the 't Hooft expansion of correlators with more than one boundaries can be computed algebraically from the correlators with a lower number of boundaries. We explicitly compute the 't Hooft expansion of then-boundary correlators forn=1,2,3. Our results reproduce previously obtained results for Jackiw-Teitelboim gravity and also the 't Hooft expansion of the exact result of the three-boundary correlator which we calculate independently in the Airy case.

Analytic continuation from Minkowski space to(2,2)split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to anS3represented as a toric fibration over the interval. Privileged scattering states of scalars organize intoSL(2,R)L?SL(2,R)Rconformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

We present a gauge theory of the conformal group in four spacetime dimensions with a non-vanishing torsion. In particular, we allow for a completely antisymmetric torsion, equivalent by Hodge duality to an axial vector whose presence does not spoil the conformal invariance of the theory, in contrast with claims of antecedent literature. The requirement of conformal invariance implies a differential condition on the aforementioned axial vector which leads to a Maxwell-like equation in a four-dimensional curved background. We also give some preliminary results in the context ofN=1four-dimensional conformal supergravity in the geometric approach, showing that if we only allow for the constraint of vanishing supertorsion all the other constraints imposed in the spacetime approach are a consequence of the closure of the Bianchi identities in superspace. This paves the way towards a future complete investigation in the direction of a conformal theory of supergravity with a non-vanishing (super)torsion.

We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

Localization approach toN=2superconformalSU(N)?SU(N)quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circularSU(N)Wilson loop?�W??. We study the subleading1/N2term in the largeNexpansion of?�W??at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to theZ2orbifold of theSU(2N)N=4SYM theory. This orbifold gauge theory should be dual to type IIB superstring inAdS5?(S5/Z2). We present a string theory argument suggesting that the1/N2term in?�W??in the orbifold theory should have the same strong-coupling asymptoticsλ3/2as in theN=4SYM case. We support this prediction by a numerical study of the localization matrix model on the gauge theory side. We also find a relation between the1/N2term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

We determine the 2-group structure constants for all the six-dimensional little string theories (LSTs) geometrically engineered in F-theory without frozen singularities. We use this result as a consistency check for T-duality: the 2- groups of a pair of T-dual LSTs have to match. When the T-duality involves a discrete symmetry twist the 2-group used in the matching is modified. We demonstrate the matching of the 2-groups in several examples.

We present and study a 4d Chern-Simons (CS) model whose gauge symmetry is encoded in a balanced Lie group crossed module. Using the derived formal set-up recently found, the model can be formulated in a way that in many respects closely parallels that of the familiar 3d CS one. In spite of these formal resemblance, the gauge invariance properties of the 4d CS model differ considerably. The 4d CS action is fully gauge invariant if the underlying base 4fold has no boundary. When it does, the action is gauge variant, the gauge variation being a boundary term. If certain boundary conditions are imposed on the gauge fields and gauge transformations, level quantization can then occur. In the canonical formulation of the theory, it is found that, depending again on boundary conditions, the 4d CS model is characterized by surface charges obeying a non trivial Poisson bracket algebra. This is a higher counterpart of the familiar WZNW current algebra arising in the 3d model. 4d CS theory thus exhibits rich holographic properties. The covariant Schroedinger quantization of the 4d CS model is performed. A preliminary analysis of 4d CS edge field theory is also provided. The toric and Abelian projected models are described in some detail.

In this paper we discuss how the Magueijo-Smolin Doubly Special Relativity proposal may obtained from a singular Lagrangian action. The deformed energy-momentum dispersion relation rises as a particular gauge, whose covariance imposes the non-linear Lorentz group action. Moreover, the additional invariant scale is present from the beginning as a coupling constant to a gauge auxiliary variable. The geometrical meaning of the gauge fixing procedure and its connection to the free relativistic particle are also described.

One of the problems in the current context of asymptotic symmetry is to extend the black hole considered to the rotating one. Therefore, we in this paper obtain a four-dimensional asymptotically flat rotating black hole solution including the displacement of supertraslation. Since it has been obtained not by solving Einstein equation but based on the already obtained supertranslated Schwarzschild black hole solution by using coordinate transformations, it is not the general solution. However, it is sure that it is `a' supertranslated rotating black hole solution as it can satisfy the Einstein equation. Then, as one of the interesting issues on the supertranslated rotating black hole, we analyze the classical gravitational perturbation with the effect of the rotating black hole by expanding with regard torfrom the infinity to the order where the effect of the rotation of the black hole can finally remain in the result.

We study a Jackiw-Teitelboim (JT) supergravity theory, defined as an Euclidean path integral over orientable supermanifolds with constant negative curvature, that was argued by Stanford and Witten to be captured by a random matrix model in theβ=2Dyson-Wigner class. We show that the theory is a double-cut matrix model tuned to a critical point where the two cuts coalesce. Our formulation is fully non-perturbative and manifestly stable, providing for explicit unambiguous computation of observables beyond the perturbative recursion relations derivable from loop equations. Our construction shows that this JT supergravity theory may be regarded as a particular combination of certain type 0B minimal string theories, and is hence a natural counterpart to another family of JT supergravity theories recently shown to be built from type 0A minimal strings. We conjecture that certain other JT supergravities can be similarly defined in terms of double-cut matrix models.