We critically examine the recent claim that the Standard Model Higgs boson H could drive inflation in agreement with observations if |H| 2 has a strong coupling ξ ∼ 10 4 to the Ricci curvature scalar. We first show that the effective theory approach upon which that claim is based ceases to be valid beyond a cutoff scale Λ = m p /ξ, where m p is the reduced Planck mass. We then argue that knowing the Higgs potential profile for the field values relevant for inflation (|H| > m p / √ ξ ≫ Λ) requires knowledge of the ultraviolet completion of the SM beyond Λ. In absence of such microscopic theory, the extrapolation of the pure SM potential beyond Λ is unwarranted and the scenario is akin to other ad-hoc inflaton potentials afflicted with significant fine-tuning. The appealing naturalness of this minimal proposal is therefore lost.

We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in terms of the operator correspondence for abelian duality. We analyze the behavior of the cosmological constant under these transformations. We also explore several examples of non-abelian duality where the classical background interpretation can be maintained for the original and the dual theory. In particular, we construct a non-abelian dual of SL(2, R) which turns out to be a three-dimensional black hole.

We estimate the very long time behaviour of correlation functions in the presence of eternal black holes. It was pointed out by Maldacena (hep-th 0106112) that their vanishing would lead to a violation of a unitarity-based bound. The value of the bound is obtained from the holographic dual field theory. The correlators indeed vanish in a semiclassical bulk approximation. We trace the origin of their vanishing to the continuum energy spectrum in the presence of event horizons. We elaborate on the two very long time scales involved: one associated with the black hole and the other with a thermal gas in the vacuum background. We find that assigning a role to the thermal gas background, as suggested in the above work, does restore the compliance with a time-averaged unitarity bound. We also find that additional configurations are needed to explain the expected time dependence of the Poincaré recurrences and their magnitude. It is suggested that, while a semiclassical black hole does reproduce faithfully "coarse grained" properties of the system, additional dynamical features of the horizon may be necessary to resolve a finer grained information-loss problem. In particular, an effectively formed stretched horizon could yield the desired results.

We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in [1] for infinite systems. We present evidence that K-complexity of ETH operators has indeed the character associated with the bulk time evolution of extremal volumes and actions. Namely, after a period of exponential growth during the scrambling period the K-complexity increases only linearly with time for exponentially long times in terms of the entropy, and it eventually saturates at a constant value also exponential in terms of the entropy. This constant value depends on the Hamiltonian and the operator but not on any extrinsic tolerance parameter. Thus K-complexity deserves to be an entry in the AdS/CFT dictionary. Invoking a concept of K-entropy and some numerical examples we also discuss the extent to which the long period of linear complexity growth entails an efficient randomization of operators.

We propose a physical interpretation of the perturbative breakdown of unitarity in timelike noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closedstring modes. In this way, we give a unified view of the string-theoretical and the fieldtheoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.

We discuss the thermal properties of string gases propagating in various D-brane backgrounds in the weak-coupling limit, and at temperatures close to the Hagedorn temperature. We determine, in the canonical ensemble, whether the Hagedorn temperature is limiting or non-limiting. This depends on the dimensionality of the D-brane, and the size of the compact dimensions. We find that in many cases the non-limiting behaviour manifest in the canonical ensemble is modified to a limiting behaviour in the microcanonical ensemble and show that, when there are different systems in thermal contact, the energy flows into open strings on the 'limiting' D-branes of largest dimensionality. Such energy densities may eventually exceed the D-brane intrinsic tension. We discuss possible implications of this for the survival of Dp-branes with large values of p in an early cosmological Hagedorn regime. We also discuss the general phase diagram of the interacting theory, as implied by the holographic and black-hole/string correspondence principles.

We consider aspects of the role of stringy scales and Hagedorn temperatures in the correspondence between various field theories and AdS-type spaces. The boundary theory is set on a toroidal world-volume to enable small scales to appear in the supergravity backgrounds also for low field-theory temperatures. We find that thermodynamical considerations tend to favour background manifolds with no string-size characteristic scales. The gravitational dynamics censors the reliable exposure of Hagedorn physics on the supergravity side, and the system does not allow the study of the Hagedorn scale by low-temperature field theories. These results are obtained following some heuristic assumptions on the character of stringy modifications to the gravitational backgrounds. A rich phenomenology appears on the supergravity side, with different string backgrounds dominating in different regions, which should have field-theoretic consequences. Six-dimensional world volumes turn out to be borderline cases from several points of view. For lower dimensional world-volumes, a fully holographic behaviour is exhibited to order 1/N 2 , and open strings in their presence are found to have a thermodynamic Hagedorn behaviour similar to that of closed strings in flat space. 09/981

We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidean AdS black hole, and the part of spacetime behind the horizon has been removed. In the flatspace limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of 'boundary entropy', the value of which decreases along the line of flow.