Spinning operators and defects in conformal field theory

Lauria, Edoardo; Meineri, Marco; Trevisani, Emilio

doi:10.1007/jhep08(2019)066

Cited by 73 publications

(103 citation statements)

References 67 publications

(334 reference statements)

Supporting

Mentioning

101

Contrasting

Order By: Relevance

“…A further ingredient that is needed to write the expression of the one-point functions is the projection of indices using the so-called z-variables [65,66]. For a symmetric traceless tensor, like the stress-energy tensor T µν , one can contract all indices with a complex vector z µ , such that z · z ≡ z µ G 0 µν z ν = 0.…”

Section: (314)mentioning

confidence: 99%

See 1 more Smart Citation

Emitted radiation and geometry

et al. 2020

View full text Add to dashboard Cite

In conformal N = 2 Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter. Keywords: N = 2 conformal SYM theories, Wilson loops, Brehmsstrahlung, rigid supersymmetry dimensions has no scale, thus the straight Wilson line can be treated as a conformal defect. The emitted radiation is computed by slightly deforming the shape of the defect.As usual, things get harder when one considers non-Abelian gauge theories, which are strongly coupled at low energies and where conformality is broken by quantum corrections. In light of this complexity, it is useful to restrict our attention to those examples of strongly interacting gauge theories which preserve conformality. These cases typically come with a larger symmetry group which includes supersymmetry, making them much more tractable. For the maximally supersymmetric theory in four dimensions, N = 4 Super Yang Mills (SYM) theory, the combination of defect techniques and supersymmetric localization led to the derivation of a beautiful formula for the Bremsstrahlung function associated with the Maldacena Wilson loop [1,2], preserving half of the supercharges. Shortly after, the same result was confirmed by an integrability computation [3,4], providing one of the few examples of a quantity that is accessible to both techniques 1 . The work of [1] heavily relied on the interpretation of the Wilson line as a superconformal defect. In particular, it was pointed out that the Bremsstrahlung function can be computed as the two-point function of an important defect operator, called the displacement operator. Furthermore, the same quantity can be related to the small angle limit of the cusp anomalous dimension, thus providing an interesting connection with massive scattering amplitudes.Similar developments allowed to find an exact expression for the Bremsstrahlung function in ABJM theory [9], a three-dimensional relative of N = 4 SYM. In that case, two superconformal Wilson lines are known (see [10] for a recent review). The immediate generalization of the Maldacena Wilson loop turns out to be 1 6 BPS [11-13] and its Bremsstrahlung function was already proposed in [14]. The maximally supersymmetric case [15], instead, involves also fermionic couplings ...

show abstract

Section: (314)mentioning

confidence: 99%

“…For tensors that are not symmetric or traceless, the procedure is a bit more intricate and a general discussion can be found in [66]. For our purposes, it is enough however to consider the case of the anti-symmetric two-index tensors.…”

Section: (314)mentioning

confidence: 99%

Emitted radiation and geometry

et al. 2020

View full text Add to dashboard Cite

show abstract

“…See footnote 2 of the published version of[27] 9. This should be contrasted with equations of motion and Ward identities in a usual QFT, were they simply relate different divergent quantities 10.…”

mentioning

confidence: 99%

“…This means the β-function we find in this section might just as well be for a theory on an interface, where there are two (possibly different) scalar theories on each side of it 27. This is done in the standard QFT way, and we have put the details on this calculation in Appendix B.…”

mentioning

confidence: 99%

Composite operators near the boundary

Prochazka

Söderberg

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3 − dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using −expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy's condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of . A. General form of a bulk-boundary correlator 32 B. Four-point correlator 33 C. Master integral 34 D. Stress-energy tensor correlator at orderĝ 35

show abstract

“…i = 0 (i = 1 · · · 2). (2.3) 12 As in subsubsection 2.1.3 of [1] we find it convenient to decompose i into its components orthogonal to the scattering plane and its components in the scattering plane…”

Section: Polarizations Of the Massless Particlesmentioning

confidence: 99%

Classification of all 3 particle S-matrices quadratic in photons or gravitons

Chakraborty

Chowdhury

Gopalka

et al. 2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We explicitly construct every kinematically allowed three particle graviton-graviton-P and photonphoton-P S-matrix in every dimension and for every choice of the little group representation of the massive particle P . We also explicitly construct the spacetime Lagrangian that generates each of these couplings. In the case of gravitons we demonstrate that this Lagrangian always involves (derivatives of) two factors of the Riemann tensor, and so is always of fourth or higher order in derivatives. This result verifies one of the assumptions made in the recent preprint [1] while attempting to establish the rigidity of the Einstein tree level S-matrix within the space of local classical theories coupled to a collection of particles of bounded spin.

show abstract

Spinning operators and defects in conformal field theory

Cited by 73 publications

References 67 publications

Emitted radiation and geometry

Emitted radiation and geometry

Composite operators near the boundary

Classification of all 3 particle S-matrices quadratic in photons or gravitons

Contact Info

Product

Resources

About