Generalised vielbeins and non-linear realisations

We briefly review why the non-linear realisation of the semi-direct product of a group with one of its representations leads to a field theory defined on a generalised space-time equipped with a generalised vielbein. We give formulae, which only involve matrix multiplication, for the generalised vielbein, the Cartan forms and their transformations. We consider the generalised space-time introduced in 2003 in the context of the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation. For this latter theory we give explicit expressions for the generalised vielbein up to and including the levels associated with the dual graviton in four, five and eleven dimensions and for the IIB theory in ten dimensions. We also compute the generalised vielbein, up to the analogous level, for the non-linear realisation of the semi-direct product of very extended SL(2) with its first fundamental representation, which is a theory associated with gravity in four dimensions.Comment: 42 page

E11 must be a symmetry of strings and branes

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in five and eleven dimensions and find the dynamical equations it predicts at low levels. Restricting these results to contain only the usual fields of supergravity and the generalised space-time to be the usual space-time we find the equations of motion of the five and eleven dimensional maximal supergravity theories. Since this non-linear realisation contains effects that are beyond the supergravity approximation and are thought to be present in an underlying theory we conclude that the low energy effective action of string and branes must possess an E11 symmetry.Comment: 17 pages, The eleven dimensional results are given in more detail and are shown to be uniquely determined. Typographical and transcription errors are also correcte

Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators

We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar $\mathcal{N}=4$ super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the $m=2$ tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the 't Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.Comment: 54 pages, 15 figure

An Operator Product Expansion for Form Factors

We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the "form factor transition". This transition is subject to a set of non-trivial bootstrap constraints, which we expect to be sufficient to fully determine it. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.Comment: 7 pages, 5 figure

An Operator Product Expansion for Form Factors II. Born level

Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.Comment: 35 pages, 4 figures, 2 ancillary files; v2: LaTeX figure issue fixe

Low-energy general relativity with torsion: a systematic derivative expansion

We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added. Final (published) versio

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Performance and Operation of the CMS Electromagnetic Calorimeter

The operation and general performance of the CMS electromagnetic calorimeter using cosmic-ray muons are described. These muons were recorded after the closure of the CMS detector in late 2008. The calorimeter is made of lead tungstate crystals and the overall status of the 75848 channels corresponding to the barrel and endcap detectors is reported. The stability of crucial operational parameters, such as high voltage, temperature and electronic noise, is summarised and the performance of the light monitoring system is presented