High Energy Physics Theory

It is well known that Jackiw-Teitelboim (JT) gravity posses the simplest theory on 2-dimensional gravity. The model has been fruitfully studied in recent years. In the present work, we investigate exact solutions for both JT and deformed JT gravity recently proposed in the literature. We revisit exact Euclidean solutions for Jackiw-Teitelboim gravity using all the non-zero components of the dilatonic equations of motion using proper integral transformation over Euclidean time coordinate. More precisely, we study exact solutions for hyperbolic coverage, cusp geometry and another compact sector of the AdS2spacetime manifold.

Two-dimensional SU(N)gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of "gluinoball" bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it toNfflavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-Nlimit decouple from the gluinoballs. We study the large-Nmeson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exactosp(1|4)symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU(N)current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD2.

We find new exact solutions of the Abelian-Higgs model coupled to General Relativity, characterized by a non-vanishing superconducting current. The solutions correspond to \textit{pp}-waves, AdS waves, and Kundt spaces, for which both the Maxwell field and the gradient of the phase of the scalar are aligned with the null direction defining these spaces. In the Kundt family, the geometry of the two-dimensional surfaces orthogonal to the superconducting current is determined by the solutions of the two-dimensional Liouville equation, and in consequence, these surfaces are of constant curvature, as it occurs in a vacuum. The solution to the Liouville equation also acts as a potential for the Maxwell field, which we integrate into a closed-form. Using these results, we show that the combined effects of the gravitational and scalar interactions can confine the electromagnetic field within a bounded region in the surfaces transverse to the current.

We compute exactly the generating function of a supersymmetric non-linear sigma model describ-ing random matrices belonging to the unitary class. Although an arbitrary source explicitly breaksthe supersymmetry, a careful analysis of the invariance of the generating function allows us to showthat it depends on only three invariant functions of the source. This generating function allows usto recover various results found in the literature. It also questions the possibility of a functionalrenormalization group study of the three-dimensional Anderson transition.

We present a novel expression for an integrated correlation function of four superconformal primaries inSU(N)N=4SYM. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. The correlator is re-expressed as a sum over a two dimensional lattice that is valid for allNand all values of the complex Yang-Mills coupling?. In this form it is manifestly invariant underSL(2,Z)Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates theSU(N)to theSU(N+1)andSU(N??)correlators. For any fixed value ofNthe correlator is an infinite series of non-holomorphic Eisenstein series,E(s;?,?¯)withs?�Z, and rational coefficients. The perturbative expansion of the integrated correlator is asymptotic and then-loop coefficient is a rational multiple ofζ(2n+1). Then=1andn=2terms agree precisely with results determined directly by integrating the expressions in one- and two-loop perturbative SYM. Likewise, the charge-kinstanton contributions have an asymptotic, but Borel summable, series of perturbative corrections. The large-Nexpansion of the correlator with fixed?is a series in powers ofN1/2?��?(?��?Z) with coefficients that are rational sums ofEswiths?�Z+1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider 't Hooft large-NYang-Mills theory. The coefficient of each order can be expanded as a convergent series inλ. For largeλthis becomes an asymptotic series with coefficients that are again rational multiples of odd zeta values. The large-λseries is not Borel summable, and its resurgent non-perturbative completion isO(exp(??λ??????)).

In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensionsD=4,5,7and 11, or equivalently theSU(N)Matrix Model. That is, the 0+1 reduction of the 10-dimensionalSU(N)Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given valueV0, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of theSU(N)constraint. We first show that their Lebesgue measure is finite, subject to restrictions onDin terms ofN. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.

We generalize soft theorems of the nonlinear sigma model beyond theO(p2)amplitudes and the coset ofSU(N)?SU(N)/SU(N). We first discuss the flavor ordering of the amplitudes for the Nambu-Goldstone bosons of a general symmetry group representation, so that we can reinterpret the knownO(p2)single soft theorem forSU(N)?SU(N)/SU(N)in the context of a general group representation. We then investigate the special case of the fundamental representation ofSO(N), where a special flavor ordering of the "pair basis" is available. We provide novel amplitude relations and a Cachazo-He-Yuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation toO(p4), where for at least two specific choices of theO(p4)operators, the leading non-vanishing pieces can be interpreted as new extended theory amplitudes involving bi-adjoint scalars, and the corresponding soft factors are the same as atO(p2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by theO(p2)Lagrangian, while any possible corrections to the subleading part are determined by theO(p4)Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.

The geometry of N=1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on the torsion tensor, the local tangent space group of O(D) x O(D) must be expanded to include a tower of higher dimension generators. These include a generator in the irreducible hook representation of the Lorentz group, which gauges the shift symmetry (or ambiguity) of the spin connection. This gauging is possible even in the purely bosonic theory, where it leads to a Lorentz curvature whose only non-vanishing pieces are the physical ones: the generalized Einstein tensor and the generalized scalar curvature. A relation to the super-Maxwell??algebra is proposed. The superspace Bianchi identities are solved up through dimension two, and the component supersymmetry transformations and equations of motion are explicitly (re)derived.

We elaborate the description of the semi-classical gravity sector of Yang-Mills matrix models on a covariant quantum FLRW background. The basic geometric structure is a frame, which arises from the Poisson structure on an underlyingS2bundle over space-time. The equations of motion for the associated Weitzenböck torsion obtained in arXiv:2002.02742 are rewritten in the form of Yang-Mills-type equations for the frame. An effective action is found which reproduces these equations of motion, which contains an Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term for the dynamical frame. An explicit rotationally invariant solution is found, which describes a gravitational field coupled to the dilaton.

We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation ofSU(N)in three dimensions. We obtain upper bounds on operator dimensions for various representations and study their dependence onN. We discover new families of kinks, one of which could be related to bosonic QED3. We then specialize to the casesN=3,4, which have been conjectured to describe a phase transition respectively in the ferromagnetic complex projective modelCP2and the antiferromagnetic complex projective modelACP3. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to small regions overlapping with the lattice predictions.