633 research outputs found
Bounds in 4D conformal field theories with global symmetry
No full textWe explore the constraining power of OPE associativity in 4D conformal field theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function (φφφ †φ†, where φ is a primary scalar operator in a given representation R. These constraints take the form of 'vectorial sum rules' for conformal blocks of operators whose representations appear in R ⊗ R and R ⊗ R̄. The coefficients in these sum rules are related to the Fierz transformation matrices for the R ⊗ R ⊗ R̄ ⊗ R̄ invariant tensors. We show that the number of equations is always equal to the number of symmetry channels to be constrained. We also analyze in detail two cases-the fundamental of SO(N) and the fundamental of SU(N). We derive the vectorial sum rules explicitly, and use them to study the dimension of the lowest singlet scalar in the φ × φ† OPE. We prove the existence of an upper bound on the dimension of this scalar. The bound depends on the conformal dimension of φ and approaches 2 in the limit dim(φ) → 1. For several small groups, we compute the behavior of the bound at dim(φ) > 1. We discuss implications of our bound for the conformal technicolor scenario of electroweak symmetry breaking. © 2011 IOP Publishing Ltd
Universal constraints on conformal operator dimensions
No full textWe continue the study of model-independent constraints on the unitary conformal field theories (CFTs) in four dimensions, initiated in. Our main result is an improved upper bound on the dimension Δ of the leading scalar operator appearing in the operator product expansion (OPE) of two identical scalars of dimension d: φ d≠1+O δ+.... In the interval 1<1.7 this universal bound takes the form Δ≤2+0.7(d-1)1/2+2. 1(d-1)+0.43(d-1)3/2. The proof is based on prime principles of CFT: unitarity, crossing symmetry, OPE, and conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2D analogue, to string theory. © 2009 The American Physical Society
What if the higgs couplings to W and Z bosons are larger than in the standard model?
No full textWe derive a general sum rule relating the Higgs coupling to W and Z bosons to the total cross section of longitudinal gauge boson scattering in I = 0; 1; 2 isospin channels. The Higgs coupling larger than in the Standard Model implies enhancement of the I = 2 cross section. Such an enhancement could arise if the Higgs sector is extended by an isospin-2 scalar multiplet including a doubly charged, singly charged, and another neutral Higgs
Central charge bounds in 4D conformal field theory
No full textWe derive model-independent lower bounds on the stress tensor central charge CT in terms of the operator content of a 4-dimensional conformal field theory. More precisely, CT is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition. © 2011 American Physical Society
The conformal bootstrap: Theory, numerical techniques, and applications
No full textConformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible due to both significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world-record determinations of critical exponents and correlation function coefficients in the Ising and O(N) models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry
Walking, weak first-order transitions, and complex CFTs
No full textWe discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a flow passing between pairs of fixed point at complex coupling. We discuss what distinguishes a real theory from a complex theory and call these fixed points complex CFTs. By using conformal perturbation theory we show how observables of the walking theory are computable by perturbing the complex CFTs. This paper discusses the general mechanism while a companion paper [1] will treat a specific and computable example: the two-dimensional Q-state Potts model with Q > 4. Concerning walking in 4d gauge theories, we also comment on the (un)likelihood of the light pseudo-dilaton, and on non-minimal scenarios of the conformal window termination
Walking, weak first-order transitions, and complex CFTs II. Two-dimensional Potts model at Q > 4
No full textWe study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q > 4. Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior present in the real Potts model at Q > 4. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter Q, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations. The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of S5-symmetric complex CFTs with central charges c ≈ 1.138±0.021i describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity
Non-gaussianity of the critical 3d Ising model
No full textLaboratoire de Physique Theórique de l'École Normale Supérieure, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, 24 rue Lhomond, 75231 Paris Cedex 05, France
Thermal production of gravitinos
No full textWe reconsider thermal production of gravitinos in the early universe, adding to previously considered 2 -> 2 gauge scatterings: (a) production via 1 -> 2 decays, allowed by thermal masses: this is the main new effect, (b) the effect of the top Yukawa coupling, and (c) a proper treatment of the reheating process. Our final result behaves physically (larger couplings give a larger rate) and is twice larger than previous results, implying e.g. a constraint on the reheating temperature that is twice as strong. Accessory results about (supersymmetric) theories at finite temperature and gravitino couplings might have some pertinence
Nedd4-2 (NEDD4L) controls intracellular Na(+) -mediated activity of voltage-gated sodium channels in primary cortical neurons
No full textNedd4-2, a HECT (homologous with E6-associated protein C-terminus)-type ubiquitin protein ligase, has been implicated in regulating several ion channels, including Navs (voltage-gated sodium channels). In Xenopus oocytes Nedd4-2 strongly inhibits the activity of multiple Navs. However, the conditions under which Nedd4-2 mediates native Nav regulation remain uncharacterized. Using Nedd4-2-deficient mice, we demonstrate in the present study that in foetal cortical neurons Nedd4-2 regulates Navs specifically in response to elevated intracellular Na+, but does not affect steady-state Nav activity. In dorsal root ganglia neurons from the same mice, however, Nedd4-2 does not control Nav activities. The results of the present study provide the first physiological evidence for an essential function of Nedd4-2 in regulating Navs in the central nervous system.Jenny A. Ekberg, Natasha A. Boase, Grigori Rychkov, Jantina Manning, Philip Poronnik and Sharad Kuma
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