On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group

We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At the planar level, the difference to the case of gauge group SU(N) is only due to certain states being projected out, however at the non-planar level novel effects appear: While 1/N-corrections in the SU(N) case are always associated with splitting and joining of spin chains, this is not so for SO(N) and Sp(N). Here the leading 1/N-corrections, which are due to non-orientable Feynman diagrams in the field theory, originate from a term in the dilatation operator which acts inside a single spin chain. This makes it possible to test for integrability of the leading 1/N-corrections by standard (Bethe ansatz) means and we carry out various such tests. For orthogonal and symplectic gauge group the dual string theory lives on the orientifold AdS5xRP5. We discuss various issues related to semi-classical strings on this background.Comment: 25 pages, 3 figures. v2: Minor clarifications, section 5 expande

Form factors of chiral primary operators at two loops in ABJ(M)

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Scrambling time from local perturbations of the eternal BTZ black hole

We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time $t_\omega$ in the large $c$ limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time $t_\omega$. In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.Comment: 37 pages, 5 figure

An algebraic approach to the scattering equations

We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism

AdS(3) holography for 1/4 and 1/8 BPS geometries

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.This research is partially supported by STFC (Grant ST/L000415/1, String theory, gauge theory & duality), by the Padova University Project CPDA119349 and by INFN