scholarly journals Surface defect, anomalies and b-extremization

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Yifan Wang
Keyword(s):  
Surface Defect ◽  
Surface Defects ◽  
Field Theories ◽  
Universal Relation ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Free Scalar ◽  
Monotonically Decrease

Abstract Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal b-anomaly analogous to the c-anomaly of 2d CFTs. The b-theorem states that b must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving $$ \mathcal{N} $$ N = (0, 2) supersymmetry, we prove a universal relation between the b-anomaly and the ’t Hooft anomaly for the U(1)r symmetry. We also establish the b-extremization principle that identifies the superconformal U(1)r symmetry from $$ \mathcal{N} $$ N = (0, 2) preserving RG flows. Together they provide a powerful tool to extract the b-anomaly of strongly coupled surface defects. To illustrate our method, we determine the b-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and ’t Hooft anomalies in defect correlation functions.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

Erratum: Synchrotron radiation in strongly coupled conformal field theories [Phys. Rev. D81, 126001 (2010)]

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
Christiana Athanasiou ◽  
Paul M. Chesler ◽  
Hong Liu ◽  
Dominik Nickel ◽  
Krishna Rajagopal
Keyword(s):  
Synchrotron Radiation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field

scholarly journals SINE-GORDON VS. MASSIVE THIRRING

1993 ◽  
Vol 08 (23) ◽  
pp. 4131-4174 ◽  
Author(s):  
TIMOTHY R. KLASSEN ◽  
EZER MELZER
Keyword(s):  
Energy Levels ◽  
Gaussian Model ◽  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Fermion Fields ◽  
S Matrix

By viewing the sine-Gordon and massive Thirring models as perturbed conformal field theories, one sees that they are different (the difference being observable, for instance, in finite-volume energy levels). The UV limit of the former (SGM) is a Gaussian model, that of the latter (MTM) a so-called fermionic Gaussian model, the compactification radius of the boson underlying both theories depending on the SG/MT coupling. (These two families of conformal field theories are related by a “twist”.) Corresponding SG and MT models contain a subset of fields with identical correlation functions, but each model also has fields the other one does not have; for example, the fermion fields of MTM are not contained in SGM, and the bosonic soliton fields of SGM are not in MTM. Our results imply, in particular, that the SGM at the so-called “free-Dirac point” β2=4π is actually a theory of two interacting bosons with diagonal S-matrix S=−1, and that for arbitrary couplings the overall sign of the accepted SG S-matrix in the soliton sector should be reversed. More generally, we draw attention to the existence of new classes of quantum field theories, analogs of the (perturbed) fermionic Gaussians models, whose partition functions are invariant only under a subgroup of the modular group. One such class comprises “fermionic versions” of the Virasoro minimal models.

scholarly journals GENERALIZED ABELIAN CHERN-SIMONS THEORIES AND THEIR CONNECTION TO CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (19) ◽  
pp. 4477-4486 ◽  
Author(s):  
MARCO A.C. KNEIPP
Keyword(s):  
Three Dimensional ◽  
Magnetic Monopoles ◽  
Field Theories ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Integral Lattice ◽  
Conformal Field ◽  
Free Scalar ◽  
Chern Simons

We discuss the generalization of Abelian Chern-Simons theories when θ-angles and magnetic monopoles are included. We map these three dimensional theories into sectors of two-dimensional conformal field theories. The introduction of θ-angles allows us to establish in a consistent fashion a connection between Abelian Chern-Simons and 2-d free scalar field compactified on a noneven integral lattice. The Abelian Chern-Simons with magnetic monopoles is related to a conformal field theory in which the sum of the charges of the chiral vertex operators inside a correlator is different from zero.

scholarly journals ON SOLITON AUTOMORPHISMS IN MASSIVE AND CONFORMAL THEORIES

1999 ◽  
Vol 11 (03) ◽  
pp. 337-359 ◽  
Author(s):  
MICHAEL MÜGER
Keyword(s):  
Field Theories ◽  
Global Symmetry ◽  
Subsequent Paper ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Symmetry Transformations ◽  
Left And Right ◽  
Necessary And Sufficient ◽  
Quasilocal Algebra

For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the left and right spacelike complements of a bounded region. We give a unified treatment by providing a necessary and sufficient condition for the existence and Poincaré covariance of soliton automorphisms which is applicable to a large class of theories. In particular, our construction applies to the QFT models with the local Fock property — in which case the latter property is the only input from constructive QFT we need — and to holomorphic conformal field theories. In conformal QFT soliton representations appear as twisted sectors, and in a subsequent paper our results will be used to give a rigorous analysis of the superselection structure of orbifolds of holomorphic theories.

NORMALIZATION FACTORS IN CONFORMAL FIELD THEORY AND THEIR APPLICATIONS

2000 ◽  
Vol 15 (04) ◽  
pp. 259-270 ◽  
Author(s):  
V. A. FATEEV
Keyword(s):  
Vacuum Expectation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Expectation Values ◽  
Conformal Field ◽  
Cylindrically Symmetric ◽  
Toda Equations ◽  
Normalization Factors

We calculate the normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We also calculate the asymptotics of cylindrically symmetric solutions of the classical Toda equations.

scholarly journals ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342020 ◽  
Author(s):  
ARPAN BHATTACHARYYA ◽  
ANINDA SINHA
Keyword(s):  
General Relativity ◽  
Entanglement Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Local Quantum ◽  
Gauge Gravity ◽  
Gravity Duality

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados–Teitelboim–Zanelli (BTZ) black hole, the Gibbons–Hawking–York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

scholarly journals Gapped Goldstones at the cut-off scale: a non-relativistic EFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
G. Cuomo ◽  
A. Esposito ◽  
E. Gendy ◽  
A. Khmelnitsky ◽  
A. Monin ◽  
...  
Keyword(s):  
Effective Field Theory ◽  
Chemical Potential ◽  
Effective Field ◽  
Energy Scale ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Charge Sector ◽  
Large Charge

Abstract At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU(2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.

Sign in / Sign up

Export Citation Format

Share Document