High Energy Physics Theory

In theories with extra dimensions, the cosmological hierarchy problem can be thought of as the unnaturally large radius of the observable universe in Kaluza-Klein units. We sketch a dynamical mechanism that relaxes this. In the early universe scenario we propose, three large spatial dimensions arise through tunneling from a 'cosmic egg', an effectively one-dimensional configuration with all spatial dimensions compact and of comparable, small size. If the string landscape is dominated by low-dimensional compactifications, cosmic eggs would be natural initial conditions for cosmology. A quantum cosmological treatment of a toy model egg predicts that, in a variant of the Hartle-Hawking state, cosmic eggs break to form higher dimensional universes with a small, but positive cosmological constant or quintessence energy. Hence cosmic egg cosmology yields a scenario in which the seemingly unnaturally small observed value of the vacuum energy can arise from natural initial conditions.

Over 30 years ago, Barrow & Tipler proposed the principle according to which the action integrated over the entire 4-manifold describing the universe should be finite. Here we explore the cosmological consequences of a related criterion, namely that semi-classical transition amplitudes from the early universe up to current field values should be well defined. On a classical level, our criterion is weaker than the Barrow-Tipler principle, but it has the advantage of being sensitive to quantum effects. We find significant consequences for early universe models, in particular: eternal inflation and strictly cyclic universes are ruled out. Within general relativity, the first phase of evolution cannot be inflationary, and it can be ekpyrotic only if the scalar field potential is trustworthy over an infinite field range. Quadratic gravity eliminates all non-accelerating backgrounds near a putative big bang (thus imposing favourable initial conditions for inflation), while the expected infinite series of higher-curvature quantum corrections eliminates Lorentzian big bang spacetimes altogether. The scenarios that work best with the principle of finite amplitudes are the no-boundary proposal, which gives finite amplitudes in all dynamical theories that we have studied, and string-inspired loitering phases. We also comment on the relationship of our proposal to the swampland conjectures.

From four-dimensionalN=4matter-coupled gauged supergravity, we study smooth time-dependent cosmological solutions interpolating between adS2?Σ2spacetime, withΣ2=S2andH2, in the infinite past and adS4spacetime in the infinite future. The solutions were obtained by solving the second-order equations of motion from all the ten gauged theories known to admitdS4solutions, of which there are two types. Type IdSgauged theories can admit bothdSsolutions as well as supersymmetricAdSsolutions while type IIdSgauged theories only admitdSsolutions. We also study the extent to which the first-order equations that solve the aforementioned second-order field equations fail to admit thedS4vacua and their associated cosmological solutions.

From five-dimensionalN=4matter-coupled gauged supergravity, smooth time-dependent cosmological solutions, connecting adS5?�d?Hd(withd=2,3) spacetime at early times to adS5spacetime at late times, are presented. The solutions are derived from the second-order equations of motion arising from all the gauged theories that can admitdS5solutions. There are eight such theories constructed from gauge groups of the formSO(1,1)?GncandSO(1,1)(n)diag?Gnc, withn=2,3, whereGncis a non-compact gauge factor whose compact part must be embedded entirely in the matter symmetry group of 5D matter-coupled supergravity. Furthermore, we analyze how the cosmological solutions and their correspondingdS5vacua cannot arise from the first-order equations that solve the second-order field equations.

We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scaleα??. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimensionD, which is however incompatible with Einstein gravity at low energies. Within anϵ-expansion aboutD=2, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution inD=4. Finally, we comment on potential cosmological implications of our findings.

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang / big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic spaceMcoupled at either end of an intervalIto a Euclidean 4D CFT onM?Iwith many fewer local degrees of freedom. We argue that in some cases, when the size ofMis much greater than the length ofI, the theory flows to a gapped / confining three-dimensional field theory onMin the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of Lorentzian 4D CFT onM?timewhose dual includes the physics of a big-bang / big-crunch cosmology. WhenMisR3, we can alternatively analytically continue one of theR3directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT isN=4SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

We argue that in certain class of coupled Sachdev-Ye-Kitaev(SYK) models the low energy physics at large N is governed by a non-local action rather than the Schwartzian action. We present a partial analytic and extensive numerical evidence for this. We find that these models are maximally chaotic and have the same residual entropy as Majorana SYK. However, thermodynamic quantities, such as heat capacity and diffusion constant are different.

We advance a covariant holographic construction based on the minimal entanglement wedge cross section, for the entanglement negativity of bipartite states inCFT1+1s dual to non static bulkAdS3geometries. In this context we obtain the holographic entanglement negativity for bipartite states inCFT1+1s dual to bulk non extremal and extremal rotating BTZ black holes and the time dependent Vaidya-AdS3geometries. Our results correctly reproduce the replica technique results for the corresponding dualCFT1+1s in the large central charge limit. Furthermore they also match exactly with the corresponding results from an alternate earlier covariant holographic entanglement negativity proposal based on an algebraic sum of the lengths of bulk extremal curves (geodesics) homologous to specific combinations of intervals for the configurations in question. This demonstrates the equivalence of the two constructions and indicates that the algebraic sum of the lengths of such bulk extremal curves (geodesics) is proportional to the minimum entanglement wedge cross section for theAdS3/CFT2scenario, which possibly extends to higher dimensions.

In the present paper the Yang-Mills theory in the first order formalism is studied. On classical level the first order formulation is equivalent to the standard second order description of the Yang-Mills theory. It is proven that both formulations remain equivalent on quantum level as well.

It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in arXiv:2008.09387. In this paper, we start to extend this analysis to the quantum realm. We identify two types of covariant singularities in field space corresponding to geodesic incompleteness and ill-defined path integrals (hereby dubbed functional singularities). We argue that the former might not be harmful after all, whilst the latter makes all observables undefined. We show that the path-integral measure is regular in any four-dimensional theory of gravity without matter or in any theory in which gravity is either absent or treated semi-classically. This might suggest the absence of functional singularities in these cases, however it can only be confirmed with a thorough analysis, case by case, of the path integral. We provide a topological and model-independent classification of functional singularities using homotopy groups and we discuss examples of theories with and without such singularities.