Constraining momentum space correlators using slightly broken higher spin symmetry

Self Cite

In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-s conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-s currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.

Section: Conformal Correlators In Spinor-helicity Variablesmentioning

confidence: 99%

Higher spin 3-point functions in 3d CFT using spinor-helicity variables

Jain

John

Mehta

et al. 2021

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“…To obtain this correlator we consider the action of Q 4 on the four-point function of scalar operators OOOO . Following the steps in the previous sections and making use of the following [62] (a similar identification of the quasi-fermionic correlator has been made in the position and Mellin spaces in [53]) and [55] respectively)…”

Section: T Ooomentioning

confidence: 99%

Relation between parity-even and parity-odd CFT correlation functions in three dimensions

Jain

John

2021

Self Cite

In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as $$ {\mathcal{W}}^3 $$ W 3 and $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ W 2 W ˜ . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

“…It would also be useful to push the LCT basis to higher values of ∆ max , in order to extract critical exponents and confirm that the critical point is described by the 3d Ising CFT. One useful tool for reaching higher values of ∆ max would be to compute the general expression for CFT three-point functions of spinning operators in momentum space, building on recent results [29,[52][53][54][55][56][57], which would greatly improve the efficiency for computing Hamiltonian matrix elements. Though in practice our Dirichlet basis states do not individually correspond to primary operators, one can construct a map between the two bases, in order to more efficiently construct matrix elements from CFT data.…”

Section: Jhep05(2021)190mentioning

confidence: 99%

Nonperturbative dynamics of (2+1)d ϕ4-theory from Hamiltonian truncation

Anand

Katz

Khandker

et al. 2021

We use Lightcone Conformal Truncation (LCT)—a version of Hamiltonian truncation — to study the nonperturbative, real-time dynamics of ϕ4-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d ϕ4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ϕ4-theory, focusing on the ℤ2 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.