A roadmap for bootstrapping critical gauge theories: decoupling  operators of conformal field theories in $d>2$ dimensions

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions d>2d>2. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of decoupling operator, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of 2d2d Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a U(1)U(1) gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both d=3d=3 and d=2+\epsilond=2+ϵ dimensions.

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Exclusion inside or at the border of conformal bootstrap continent

International Journal of Modern Physics A ◽

10.1142/s0217751x20500360 ◽

2020 ◽

Vol 35 (06) ◽

pp. 2050036

Author(s):

Yu Nakayama

Keyword(s):

Bound States ◽

Pauli Exclusion Principle ◽

Higher Dimensions ◽

Two Dimensions ◽

Field Theories ◽

Exclusion Principle ◽

Conformal Field Theories ◽

Conformal Field ◽

Conformal Bootstrap ◽

Anomalous Dimensions

How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing nontrivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at the (second) kink. In higher dimensions, it more or less saturates the bound but it may be slightly inside.

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Constructing Carrollian CFTs

Journal of High Energy Physics ◽

10.1007/jhep03(2021)194 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Nishant Gupta ◽

Nemani V. Suryanarayana

Keyword(s):

Scalar Fields ◽

Higher Dimensions ◽

Field Theories ◽

Conformal Field Theories ◽

Relativistic Limit ◽

Conformal Field ◽

Local Symmetries ◽

Derivatives Of ◽

Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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Bootstrap experiments on higher dimensional CFTs

International Journal of Modern Physics A ◽

10.1142/s0217751x18500367 ◽

2018 ◽

Vol 33 (07) ◽

pp. 1850036 ◽

Cited By ~ 7

Author(s):

Yu Nakayama

Keyword(s):

Empirical Relationship ◽

Adjoint Representation ◽

Field Theories ◽

Conformal Field Theories ◽

Time Dimension ◽

Unitarity Bound ◽

Conformal Field ◽

Dimension Formula ◽

Conformal Bootstrap ◽

Higher Dimensional

Recent programs on conformal bootstrap suggest an empirical relationship between the existence of nontrivial conformal field theories and nontrivial features such as a kink in the unitarity bound of conformal dimensions in the conformal bootstrap equations. We report the existence of nontrivial kink-like behaviors in the unitarity bound of scalar operators in the adjoint representation of the [Formula: see text] symmetric conformal field theories. They have interesting properties: (1) the kink-like behaviors exist in [Formula: see text] dimensions; (2) the location of kink-like behaviors are when the unitarity bound hits the space–time dimension [Formula: see text]; (3) there exists a “conformal window” of [Formula: see text], where [Formula: see text] in [Formula: see text] and [Formula: see text] in [Formula: see text].

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Liouville conformal field theories in higher dimensions

Journal of High Energy Physics ◽

10.1007/jhep06(2018)119 ◽

2018 ◽

Vol 2018 (6) ◽

Cited By ~ 5

Author(s):

Tom Levy ◽

Yaron Oz

Keyword(s):

Higher Dimensions ◽

Field Theories ◽

Conformal Field Theories ◽

Conformal Field

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REPRESENTATIONS OF COMPOSITE BRAIDS AND INVARIANTS FOR MUTANT KNOTS AND LINKS IN CHERN-SIMONS FIELD THEORIES

Modern Physics Letters A ◽

10.1142/s0217732395001769 ◽

1995 ◽

Vol 10 (22) ◽

pp. 1635-1658 ◽

Cited By ~ 25

Author(s):

P. RAMADEVI ◽

T.R. GOVINDARAJAN ◽

R.K. KAUL

Keyword(s):

Field Theories ◽

Simons Theory ◽

Conformal Field Theories ◽

Abelian Gauge ◽

Gauge Groups ◽

Knot Invariants ◽

Conformal Field ◽

Chern Simons ◽

Knots And Links ◽

Chern Simons Theory

We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-Abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and links, we study Murakami (symmetrized version) r-strand composite braids. Salient features of the theory of such composite braids are presented. Representations of generators for these braids are obtained by exploiting properties of Hilbert spaces associated with the correlators of Wess-Zumino conformal field theories. The r-composite invariants for the knots are given by the sum of elementary Chern-Simons invariants associated with the irreducible representations in the product of r representations (allowed by the fusion rules of the corresponding Wess-Zumino conformal field theory) placed on r individual strands of the composite braid. On the other hand, composite invariants for links are given by a weighted sum of elementary multicolored Chern-Simons invariants. Some mutant links can be distinguished through the composite invariants, but mutant knots do not share this property. The results, though developed in detail within the framework of SU(2) Chern-Simons theory are valid for any other non-Abelian gauge groups.

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