1,720,989 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
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
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
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
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
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
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
A scaling theory for the long-range to short-range crossover and an infrared duality
No full textWe study the second-order phase transition in the d-dimensional Ising model with long-range interactions decreasing as a power of the distance . For s below some known value , the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of s. At , the phase transition crosses over to the short-range universality class. While the location of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality
Long-Range Critical Exponents near the Short-Range Crossover
No full textThe d-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power 1/rd+s, admits a second-order phase transition with continuously varying critical exponents. At s=s∗, the phase transition crosses over to the usual short-range universality class. The standard field-theoretic description of this family of models is strongly coupled at the crossover. We find a new description, which is instead weakly coupled near the crossover, and use it to compute critical exponents. The existence of two complementary UV descriptions of the same long-range fixed point provides a novel example of infrared duality
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