scholarly journals Two-dimensional O(n) models and logarithmic CFTs

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Victor Gorbenko ◽  
Bernardo Zan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Negative Norm ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Bootstrap Approach ◽  
Continuous Range ◽  
Relevant Operator

Abstract We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG flow. When n is equal to two, which corresponds to the Kosterlitz-Thouless critical theory, the fixed points collide. We find that for n generic these CFTs are logarithmic and contain negative norm states; in particular, the O(n) currents belong to a staggered logarithmic multiplet. Using a conformal bootstrap approach we trace how the negative norm states decouple at n = 2, restoring unitarity. The IR fixed point possesses a local relevant operator, singlet under all known global symmetries of the CFT, and, nevertheless, it can be reached by an RG flow without tuning. Besides, we observe logarithmic correlators in the closely related Potts model.

scholarly journals Perturbative and nonperturbative studies of CFTs with MN global symmetry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Johan Henriksson ◽  
Andreas Stergiou
Keyword(s):  
Fixed Points ◽  
Numerical Data ◽  
Three Dimensions ◽  
Global Symmetry ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
State Of Affairs ◽  
Perturbative Limit ◽  
Good Agreement

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_nMNm,n=O(m)n⋊Sn global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2m=n=2 suggest the existence of two non-trivial fixed points, while the \varepsilonε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters mm and nn, with critical exponents in good agreement with experimental determinations in the m=n=2m=n=2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters mm and nn. We find that one family of kinks approaches a perturbative limit as mm increases, and using large spin perturbation theory we construct a large mm expansion that fits well with the numerical data. This new expansion, akin to the large NN expansion of critical O(N)O(N) models, is compatible with the fixed point found in the \varepsilonε expansion. For the other family of kinks, we find that it persists only for n=2n=2, where for large mm it approaches a non-perturbative limit with \Delta_\phi\approx 0.75Δϕ≈0.75. We investigate the spectrum in the case \ensuremath{M N}_{100,2}MN100,2 and find consistency with expectations from the lightcone bootstrap.

scholarly journals SIMPLE CURRENTS, MODULAR INVARIANTS AND FIXED POINTS

1990 ◽  
Vol 05 (15) ◽  
pp. 2903-2952 ◽  
Author(s):  
A.N. SCHELLEKENS ◽  
S. YANKIELOWICZ
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Fixed Points ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Modular Invariants ◽  
Simple Currents

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals Quantum dimension as entanglement entropy in two dimensional conformal field theories

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
Song He ◽  
Tokiro Numasawa ◽  
Tadashi Takayanagi ◽  
Kento Watanabe
Keyword(s):  
Entanglement Entropy ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field

SOME LANDAU-GINZBURG MODELS FROM CONFORMAL FIELD THEORY

1990 ◽  
Vol 05 (12) ◽  
pp. 2343-2358 ◽  
Author(s):  
KEKE LI
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Operator Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Coset Models ◽  
Marginal Deformation

A method of constructing critical (fixed point) Landau-Ginzburg action from operator algebra is applied to several classes of conformal field theories, including lines of c = 1 models and the coset models based on SU(2) current algebra. For the c = 1 models, the Landau-Ginzberg potential is argued to be physically consistent, and it resembles a modality-one singularity with modal deformation representing exactly the marginal deformation. The potentials for the coset models manifestly possess correct discrete symmetries.

scholarly journals TWO-DIMENSIONAL FRACTIONAL SUPERSYMMETRIC CONFORMAL FIELD THEORIES AND THE TWO-POINT FUNCTIONS

2001 ◽  
Vol 16 (12) ◽  
pp. 2165-2173 ◽  
Author(s):  
FARDIN KHEIRANDISH ◽  
MOHAMMAD KHORRAMI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Closed Subalgebra

A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by (L-1,L0,G-1/3) and [Formula: see text], the two-point functions of the component fields of supermultiplets are calculated.

scholarly journals ON THE CONFORMAL ANOMALY FROM HIGHER DERIVATIVE GRAVITY IN AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (03) ◽  
pp. 413-428 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Einstein Gravity ◽  
Low Energy ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Higher Derivative

We follow Witten's proposal1 in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above (d + 1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L =aR2 + bRμνRμν + Λ (even when a=0 or b=0) is five-dimensional bulk theory for [Formula: see text] super-Yang–Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of [Formula: see text] supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).

Sign in / Sign up

Export Citation Format

Share Document