scholarly journals Anomalous dimensions at large charge for U(N)×U(N) theory in three and four dimensions

2021 ◽  
Vol 104 (10) ◽  
Author(s):  
I. Jack ◽  
D. R. T. Jones
Keyword(s):  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Large Charge

scholarly journals Six-dimensional ultraviolet completion of the ℂℙ(N) σ model at two loops

2020 ◽  
Vol 35 (22) ◽  
pp. 2050188
Author(s):  
J. A. Gracey
Keyword(s):  
Renormalization Group ◽  
Quantum Electrodynamics ◽  
Matter Field ◽  
Coupling Constants ◽  
Universal Theory ◽  
Gauge Parameter ◽  
Loop Analysis ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Group Functions

We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

scholarly journals Boundary conformal field theory at large charge

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Gabriel Cuomo ◽  
Márk Mezei ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Background Field ◽  
Effective Field ◽  
Three Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Fisher Model ◽  
Large Charge

Abstract We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

scholarly journals Anomalous dimensions at large charge in d=4 O(N) theory

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
I. Jack ◽  
D. R. T. Jones
Keyword(s):  
Anomalous Dimensions ◽  
Large Charge

scholarly journals General scalar renormalisation group equations at three-loop order

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Tom Steudtner
Keyword(s):  
Specific Model ◽  
Renormalisation Group ◽  
Loop Order ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
General Scalar ◽  
Mass Terms ◽  
Scalar Theories

Abstract For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

scholarly journals A GEOMETRICAL INTERPRETATION OF RENORMALIZATION GROUP FLOW

1994 ◽  
Vol 09 (08) ◽  
pp. 1261-1286 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Euclidean Space ◽  
Point Of View ◽  
Dimensional Euclidean Space ◽  
Lie Derivative ◽  
Coupling Constant ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Definition Of ◽  
Group Flow

The renormalization group (RG) equation in D-dimensional Euclidean space, RD, is analyzed from a geometrical point of view. A general form of the RG equation is derived which is applicable to composite operators as well as tensor operators (on RD) which may depend on the Euclidean metric. It is argued that physical N-point amplitudes should be interpreted as rank N covariant tensors on the space of couplings, [Formula: see text], and that the RG equation can be viewed as an equation for Lie transport on [Formula: see text] with respect to the vector field generated by the β functions of the theory. In one sense it is nothing more than the definition of a Lie derivative. The source of the anomalous dimensions can be interpreted as being due to the change of the basis vectors on [Formula: see text] under Lie transport. The RG equation acts as a bridge between Euclidean space and coupling constant space in that the effect on amplitudes of a diffeomorphism of RD (that of dilations) is completely equivalent to a diffeomorphism of [Formula: see text] generated by the β functions of the theory. A form of the RG equation for operators is also given. These ideas are developed in detail for the example of massive λφ4 theory in four dimensions.

DIMENSIONAL REDUCTION AND THE NON-TRIVIALITY OF λϕ4 IN FOUR DIMENSIONS AT HIGH TEMPERATURE

1993 ◽  
Vol 08 (19) ◽  
pp. 1779-1793 ◽  
Author(s):  
DENJOE O’CONNOR ◽  
C.R. STEPHENS ◽  
F. FREIRE
Keyword(s):  
High Temperature ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Infinite Temperature ◽  
Second Order Phase Transition

λϕ4 theory in four dimensions is shown perturbatively to have a non-trivial fixed point at finite temperature, the relevant anomalous dimensions at the second order phase transition being the three-dimensional ones. We emphasize the importance of having renormalization schemes and a renormalization group equation that can explicitly take into account the fact that the degrees of freedom of a theory may be qualitatively different at different scales. By applying such considerations to finite temperature λϕ4 where the low temperature degrees of freedom are effectively four-dimensional and the high temperature ones three-dimensional we are able to follow perturbatively the theory from zero to infinite temperature.

scholarly journals 𝒩 = 2 dualities and Z-extremization in three dimensions

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Brian Willett ◽  
Itamar Yaakov
Keyword(s):  
Three Dimensions ◽  
Partition Functions ◽  
Recent Proposal ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Seiberg Duality ◽  
Real Mass ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We use localization techniques to study duality in 𝒩 = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

FACT-2 – The Frankfurt Adaptive Concentration Test

2009 ◽  
Vol 25 (2) ◽  
pp. 73-82 ◽  
Author(s):  
Frank Goldhammer ◽  
Helfried Moosbrugger ◽  
Sabine A. Krawietz
Keyword(s):  
Convergent Validity ◽  
Four Dimensions ◽  
Measurement Models ◽  
Cognitive Failures ◽  
Concentration Test ◽  
Cognitive Failures Questionnaire

The Frankfurt Adaptive Concentration Test (FACT-2) requires discrimination between geometric target and nontarget items as quickly and accurately as possible. Three forms of the FACT-2 were constructed, namely FACT-I, FACT-S, and FACT-SR. The aim of the present study was to investigate the convergent validity of the FACT-SR with self-reported cognitive failures. The FACT-SR and the Cognitive Failures Questionnaire (CFQ) were completed by 191 participants. The measurement models confirmed the concentration performance, concentration accuracy, and concentration homogeneity dimensions of FACT-SR. The four dimensions of the CFQ (i.e., memory, distractibility, blunders, and names) were not confirmed. The results showed moderate convergent validity of concentration performance, concentration accuracy, and concentration homogeneity with two CFQ dimensions, namely memory and distractibility/blunders.

Sign in / Sign up

Export Citation Format

Share Document