Spinning strings and integrable spin chains in the AdS/CFT correspondence

In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display its reformulation in terms of a Heisenberg s=1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way we comment on further developments and generalizations of the subject and point to the relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2: improvements in the text and references adde

The Varieties of Ought-implies-Can and Deontic STIT Logic

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings

A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

Holographic Meson Melting

The plasma phase at high temperatures of a strongly coupled gauge theory can be holographically modelled by an AdS black hole. Matter in the fundamental representation and in the quenched approximation is introduced through embedding D7-branes in the AdS-Schwarzschild background. Low spin mesons correspond to the fluctuations of the D7-brane world volume. As is well known by now, there are two different kinds of embeddings, either reaching down to the black hole horizon or staying outside of it. In the latter case the fluctuations of the D7-brane world volume represent stable low spin mesons. In the plasma phase we do not expect mesons to be stable but to melt at sufficiently high temperature. We model the late stages of this meson melting by the quasinormal modes of D7-brane fluctuations for the embeddings that do reach down to the horizon. The inverse of the imaginary part of the quasinormal frequency gives the typical relaxation time back to equilibrium of the meson perturbation in the hot plasma. We briefly comment on the possible application of our model to quarkonium suppression.Comment: 25+1 pages, 6 figures; v4: references adde

Failure of interpolation in the intuitionistic logic of constant domains

This paper shows that the interpolation theorem fails in the intuitionistic logic of constant domains. This result refutes two previously published claims that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text thouroughly reworked in terms of notation and style, historical notes as well as some other minor details adde