High Energy Physics Theory

In this paper we begin mapping out the space of rank-2N=2superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum field-theoretic tools, thus providing a precious case study to probe the completeness of the current understanding of SCFTs, primarily derived from string theory constructions. Here, we collect and systematize a large amount of field theoretic data characterizing each theory. We also provide a detailed description of each case and determine the theories' Coulomb, Higgs and Mixed branch stratification. The theories naturally organize themselves into series connected by RG flows but which have gaps suggesting that our current understanding is not complete.

The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the1/Nexpansion, and at all loops. By investigating the large order behaviour of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the largeNtrans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the1/Nexpansion.

We investigate the Bethe-Ansatz (BA) approach to the superconformal index ofN=4supersymmetric Yang-Mills with SU(N) gauge group in the context of finite rank,N. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations (BAE) in recovering the exact index forN=2,3. We classify the BAE solutions as standard (corresponding to a freely acting orbifoldT2/Zm?Zn) and non-standard. ForN=2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, forN??, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

The unitarity of time evolution, or colloquially the conservation of probability, sits at the heart of our descriptions of fundamental interactions via quantum field theory. The implications of unitarity for scattering amplitudes are well understood, for example through the optical theorem and cutting rules. In contrast, the implications for in-in correlators in curved spacetime and the associated wavefunction of the universe, which are measured by cosmological surveys, are much less transparent. For fields of any mass in de Sitter spacetime with general local interactions, which need not be invariant under de Sitter isometries, we show that unitarity implies an infinite set of relations among the coefficientsψnof the wavefunction of the universe withnfields, which we name Cosmological Optical Theorem. For contact diagrams, our result dictates the analytic structure ofψnand strongly constrains its form. For example, any correlator with an odd number of conformally-coupled scalar fields and any number of massless scalar fields must vanish. For four-point exchange diagrams, the Cosmological Optical Theorem yields a simple and powerful relation betweenψ3andψ4, or equivalently between the bispectrum and trispectrum. As explicit checks of this relation, we discuss the trispectrum in single-field inflation from graviton exchange and self-interactions. Moreover, we provide a detailed derivation of the relation between the total-energy pole of cosmological correlators and flat-space amplitudes. We provide analogous formulae for sub-diagram singularities. Our results constitute a new, powerful tool to bootstrap cosmological correlators.

Using Perelman's approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum, and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the later scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.

We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in \cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in \cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian.

We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice-punctured torus times a 9D Minkowski spacetime. It corresponds to a M2-brane formulated in 11D space with ten non compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermenbrane in the target space are treated rigorously. The nontrivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generate a cosmological term on the Hamiltonian of the theory.The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in 9D. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the(1,1)?�knotsassociated to the monodromies.

In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the Kustaanheimo-Stiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.

We examine the Regge limit of holographic 4-point correlation functions in AdS3?S3involving two heavy and two light operators. In this kinematic regime such correlators can be reconstructed from the bulk phase shift accumulated by the light probe as it traverses the geometry dual to the heavy operator. We work perturbatively -- but to arbitrary orders -- in the ratio of the heavy operator's conformal dimension to the dual CFT2's central charge, thus going beyond the low order results of arXiv:1812.03120 and arXiv:2007.12118. In doing so, we derive all-order relations between the bulk phase shift and the Regge limit OPE data of a class of heavy-light multi-trace operators exchanged in the cross-channel. Furthermore, we analyse two examples for which the relevant 4-point correlators are known explicitly to all orders: firstly the case of heavy operators dual to AdS3conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.

We prove the equivalence between two traditional approaches to the classical mechanics of a massive spinning particle in special relativity. One is the spherical top model of Hanson and Regge, recast in a Hamiltonian formulation with improved treatment of covariant spin constraints. The other is the massive twistor model, slightly generalized to incorporate the Regge trajectory relating the mass to the total spin angular momentum. We establish the equivalence by computing the Dirac brackets of the physical phase space carrying three translation and three rotation degrees of freedom. Lorentz covariance and little group covariance uniquely determine the structure of the physical phase space. The Regge trajectory does not affect the phase space but enters the equations of motion. Upon quantization, the twistor model produces a spectrum that agrees perfectly with the massive spinor-helicity description proposed by Arkani-Hamed, Huang and Huang for scattering amplitudes for all masses and spins.