High Energy Physics Theory

We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum toO(G2), which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

We present a simple compact formula for a topologically nontrivial mapS7?�Spin(7)associated with the fiber bundleSpin(7)??G2S7. The homotopy group?7[Spin(7)]=Zbrings about the topologically nontrivial 8-dimensional gauge field configurations that belong to the algebraspin(7)-- the instantons. Similar constructions for other algebras in different dimensions are briefly discussed.

We extend and generalise the string corrections to the EM memory to the Type I superstring including spin effects. Very much as in the simpler bosonic string context, the relevant corrections are non-perturbative inα??, slowly decaying (as1/R) at large distances and modulated in retarded timeu=t?�R. For spinNstates in the first Regge trajectory they entail a sequence ofNderivatives wrtuon the `parent'N=0amplitude. We also briefly discuss how to include loop effects, that broaden and shift the string resonances, and how to modify our analysis for macroscopic semi-classical quasi-BPS coherent states, whose collisions may lead to detectable string memory signals in viable Type I models.

Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales asO(1). We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.

We consider the sphere free energyF(b;mI)inN=6ABJ(M) theory deformed by both three real massesmIand the squashing parameterb, which has been computed in terms of anNdimensional matrix model integral using supersymmetric localization. We show that settingm3=ib??b??2relatesF(b;mI)to the round sphere free energy, which implies infinite relations betweenmIandbderivatives ofF(b;mI)evaluated atmI=0andb=1. ForN=8ABJ(M) theory, these relations fix all fourth order and some fifth order derivatives in terms of derivatives ofm1,m2, which were previously computed to all orders in1/Nusing the Fermi gas method. This allows us to compute??4bF|b=1and??5bF|b=1to all orders in1/N, which we precisely match to a recent prediction to sub-leading order in1/Nfrom the holographically dualAdS4bulk theory.

We investigate a class of reducible yet indecomposable modules over theN=2superconformal algebras. These so-called staggered modules exhibit a non-diagonalisable action of the Virasoro modeL0. Using recent results on the coset construction ofN=2minimal models, we explicitly construct such modules for central chargesc=??andc=??. We also describe spectral-flow orbits and symmetries of the families of staggered modules which arise via the coset.

The physical principles of causality and unitarity put strong constraints on the analytic structure of the flat-space S-matrix. In particular, these principles give rise to the Steinmann relations, which require that the double discontinuities of scattering amplitudes in partially-overlapping momentum channels vanish. Conversely, at cosmological scales, the imprint of causality and unitarity is in general less well understood---the wavefunction of the universe lives on the future space-like boundary, and has all time evolution integrated out. In the present work, we show how the flat-space Steinmann relations emerge from the structure of the wavefunction of the universe, and derive similar relations that apply to the wavefunction itself. This is done within the context of scalar toy models whose perturbative wavefunction has a first-principles definition in terms of cosmological polytopes. In particular, we use the fact that the scattering amplitude is encoded in the scattering facet of cosmological polytopes, and that cuts of the amplitude are encoded in the codimension-one boundaries of this facet. As we show, the flat-space Steinmann relations are thus implied by the non-existence of codimension-two boundaries at the intersection of the boundaries associated with pairs of partially-overlapping channels. Applying the same argument to the full cosmological polytope, we also derive Steinmann-type constraints that apply to the full wavefunction of the universe. These arguments show how the combinatorial properties of cosmological polytopes lead to the emergence of flat-space causality in the S-matrix, and provide new insights into the analytic structure of the wavefunction of the universe.

We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, we derive the associated Schrödinger equation. The resulting equations show that massive scalar particles must be conformally coupled to gravity in a theory of quantum gravity. We conclude with a discussion of some prospects of the stochastic framework.

We revisit gravitational particle production from the Stokes phenomenon viewpoint, which helps us make a systematic way to understand asymptotic behavior of mode functions in time-dependent background. One of our purposes of this work is to make the method more practical for evaluation of non-perturbative particle production rate. In particular, with several examples of time-dependent backgrounds, we introduce some approximation methods that make the analysis more practical. Specifically, we consider particle production in simple expanding backgrounds, preheating afterR2inflation, and a transition model with smoothly changing mass. As we find several technical issues in analyzing the Stokes phenomenon of each example, we discuss how to simplify the problems while showing the accuracy of analytic estimation under the approximations we make.