184 research outputs found
Conformal Field Theories in Fractional Dimensions
We study the conformal bootstrap in fractional space-time dimensions,
obtaining rigorous bounds on operator dimensions. Our results show strong
evidence that there is a family of unitary CFTs connecting the 2D Ising model,
the 3D Ising model, and the free scalar theory in 4D. We give numerical
predictions for the leading operator dimensions and central charge in this
family at different values of D and compare these to calculations of phi^4
theory in the epsilon-expansion.Comment: 11 pages, 4 figures - references updated - one affiliation modifie
Jet Physics from Static Charges in AdS
Soft interactions with high-energy jets are explored in radial coordinates
which exploit the approximately conformal behavior of perturbative gauge
theories. In these coordinates, the jets, approximated by Wilson lines, become
static charges in Euclidean AdS. The anomalous dimension of the corresponding
Wilson line operator is then determined by the potential energy of the charges.
To study these Wilson lines we introduce a "conformal gauge" which does not
have kinetic mixing between radial and angular directions, and show that a
number of properties of Wilson lines are reproduced through relatively simple
calculations. For example, certain non-planar graphs involving multiple Wilson
lines automatically vanish. We also discuss the linear growth of the charges'
imaginary potential energy with separation, and a relationship between Wilson
line diagrams and Witten diagrams.Comment: 34 pages, 7 figures; V2: minor edits, added reference
Carving out OPE space and precise O(2) model critical exponents
We develop new tools for isolating CFTs using the numerical bootstrap. A âcutting surfaceâ algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8Ï discrepancy between theory and experiment
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Jet physics from static charges in AdS space
Soft interactions with high-energy jets are explored in radial coordinates which exploit the approximately conformal behavior of perturbative gauge theories. In these coordinates, the jets, approximated by Wilson lines, become static charges in Euclidean AdS. The anomalous dimension of the corresponding Wilson line operator is then determined by the potential energy of the charges. To study these Wilson lines we introduce a âconformal gaugeâ which does not have kinetic mixing between radial and angular directions, and show that a number of properties of Wilson lines are reproduced through relatively simple calculations. For example, certain non-planar graphs involving multiple Wilson lines automatically vanish. We also discuss the linear growth of the chargesâ imaginary potential energy with separation, and a relationship between Wilson line diagrams and Witten diagrams.Physic
Seed conformal blocks in 4D CFT
We compute in closed analytical form the minimal set of \u201cseed\u201d conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (\u2113, \u2113) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, |\u2113 12 \u2113|) and one (|\u2113 12 \u2113|, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (\u2113, \u2113), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = |\u2113 12 \u2113| and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories
Bounds on 4D Conformal and Superconformal Field Theories
We derive general bounds on operator dimensions, central charges, and OPE
coefficients in 4D conformal and N=1 superconformal field theories. In any CFT
containing a scalar primary phi of dimension d we show that crossing symmetry
of implies a completely general lower bound on the central
charge c >= f_c(d). Similarly, in CFTs containing a complex scalar charged
under global symmetries, we bound a combination of symmetry current two-point
function coefficients tau^{IJ} and flavor charges. We extend these bounds to
N=1 superconformal theories by deriving the superconformal block expansions for
four-point functions of a chiral superfield Phi and its conjugate. In this case
we derive bounds on the OPE coefficients of scalar operators appearing in the
Phi x Phi* OPE, and show that there is an upper bound on the dimension of Phi*
Phi when dim(Phi) is close to 1. We also present even more stringent bounds on
c and tau^{IJ}. In supersymmetric gauge theories believed to flow to
superconformal fixed points one can use anomaly matching to explicitly check
whether these bounds are satisfied.Comment: 47 pages, 9 figures; V2: small corrections and clarification
Superconformal Flavor Simplified
A simple explanation of the flavor hierarchies can arise if matter fields
interact with a conformal sector and different generations have different
anomalous dimensions under the CFT. However, in the original study by Nelson
and Strassler many supersymmetric models of this type were considered to be
'incalculable' because the R-charges were not sufficiently constrained by the
superpotential. We point out that nearly all such models are calculable with
the use of a-maximization. Utilizing this, we construct the simplest
vector-like flavor models and discuss their viability. A significant constraint
on these models comes from requiring that the visible gauge couplings remain
perturbative throughout the conformal window needed to generate the
hierarchies. However, we find that there is a small class of simple flavor
models that can evade this bound.Comment: 43 pages, 1 figure; V3: small corrections and clarifications,
references adde
Deconstructing Conformal Blocks in 4D CFT
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few \u201cseed\u201d correlators, simplifying dramatically the computation needed to bootstrap tensor correlators. \ua9 2015, The Author(s)
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