We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision.We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers.For N = 1 superconformal theories the one point function for states created by the Rcurrent or the stress tensor are determined by the two parameters a and c characterizing the conformal anomaly. Demanding that the measured energies are positive we get bounds on a/c. We also give a prescription for computing the energy and charge correlation functions in theories that have a gravity dual. The prescription amounts to probing the falling string state as it crosses the AdS horizon with gravitational shock waves. In the leading, two derivative, gravity approximation the energy is uniformly distributed on the sphere at infinity, with no fluctuations. We compute the stringy corrections and we show that they lead to small, non-gaussian, fluctuations in the energy distribution. Corrections to the one point functions or antenna patterns are related to higher derivative corrections in the bulk. Z µ Z −1 +Z 4 , µ = 0, 1, 2, 3. The metric induced on this surface, (2.3), by the R 2,4 metric is fixed up to an overallx-dependent factor. We can choose a metric by choosing a "gauge condition" such as 3 This type of coordinates has also been studied in [17]. 4 Note that Z −1 is the "minus one" component of the vector Z and it does not denote the inverse of Z. Hopefully, this notation will not cause confusion.

Studies of N = 4 super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain. These spin chains have fundamental "magnon" excitations which obey a dispersion relation that is periodic in the momentum of the magnons. This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling. Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description. The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle. We use these results to compute the energy of a spinning string. We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory. We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture. We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite. *

We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d conformal group, but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near horizon geometry of any extremal black hole are identical to those of a 2d field theory with chiral scaling. We consider two examples: black holes in warped AdS 3 in topologically massive gravity, and in string theory. In both cases, the density of states in the 2d field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.arXiv:1210.0539v2 [hep-th]

The conserved magnetic flux of U(1) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are seven dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfven modes. Finally, we demonstrate that a non-trivial truncation of the theory can be performed at low temperatures compared to the magnetic field: this theory has an emergent Lorentz invariance along magnetic field lines, and hydrodynamic fluctuations are now parametrized by a fluid tensor rather than a fluid velocity. Throughout, no assumption is made of weak electromagnetic coupling. Thus, our theory may have phenomenological relevance for dense electromagnetic plasmas.Comment: 21 pages, 4 figures; v2: counting of transport coefficients fixed, errors in Kubo formulae and other typos correcte