The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity operators apart from the conformal generators play an important role in fixing their functional form. The equations take the form of first order Euler equations which in addition to the usual solutions that are rational, also possess weak solutions which are distributional in nature. We found two distinct classes of distributional solutions to these equations that play an important role in our analysis. For instance, in the case of three point functions, the distributional solutions are indeed the ones realized by the CFT correlators. We also extend our analysis to parity odd Wightman functions which take an interesting form in twistor space. We verify our results by systematically analyzing the corresponding Wightman functions in momentum space and spinor helicity variables and matching with the twistor results via a half-Fourier transform.

India

Aswini Bala

Sachin Jain

K. Dhruva

Deep Mazumdar

Vibhor Singh

3D conformal field theory in twistor space

<p>Nontrivial conformal field theories are rare. Motivated by the recent construction of a local higher-spin gravity in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>AdS</mi><mn>4</mn></msub></math>—chiral higher-spin gravity—we begin to identify its anti–de Sitter/conformal field theory (AdS/CFT) dual theory that has to be a closed subsector of Chern-Simons matter theories, thereby shedding more light on this class of CFTs and the dualities that relate them. We show that at the level of two- and three-point functions the sub-CFT can be defined as a limit of Chern-Simons matter theories where only correlators with the total positive (or negative) helicity are kept. We also discuss extension to higher orders and list a number of nontrivial predictions from the bulk.</p>

Dhruva K. S

Belgium

Evgeny Skvortsov

Hidden sectors of Chern-Simons matter theories and exact holography

In this paper, we investigate if it is possible to express correlation functions in Large N Chern-Simons (CS) matter theories/ Slightly Broken Higher Spin (SBHS) theories purely in terms of single trace twist conformal blocks (TCBs). For this, we first develop the machinery for spinning TCBs. We do this both by explicitly solving the spinning TCB eigenvalue equation taking into account consistency with the operator product expansion (OPE) and crossing symmetry, and also by employing weight shifting and spin raising operators and acting with them on scalar seeds. Using these results we show that spinning correlators in theories with exact higher spin symmetry can be entirely expressed in terms of single trace TCBs. However, when the higher spin symmetry is slightly broken at large-N, even though the scalar four-point function is given by single-trace TCBs, the spinning correlators in general, are not. Our results suggest that it may be possible to identify a sub-sector of SBHS theory which has a local bulk dual.

A spin on the bulk locality of Slightly Broken Higher Spin theories

We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the α-vacuum, in single-field slow-roll inflation. The α-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in α-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar α-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in α-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with α-vacua correlators.

Arhum Ansari

Pinak Banerjee

Prateksh Dhivakar

Nilay Kundu

Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

In this paper, we develop a momentum super space formalism for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1, 2 theories. We discover interesting double copy relations in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 super-correlators. Further, we discovered super double copy relations that take us from   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Dhruva K.S

Shivang Yadav

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

Bootstrapping in Quantum Mechanics uses positivity condition to derive the eigenspectum. For non-hermitian systems usual positivity condition does not work. In this paper we define positivity condition for special class of non-hermitian Hamiltonian, the PT symmetric Hamiltonian. We illustrate this modified positivity condition with several examples and obtain eigenspectrum.

Sakil Khan

Yuv Agarwal

Devjyoti Tripathy

Bootstrapping PT symmetric quantum mechanics

We develop a systematic method to constrain any n-point correlation function of spinning operators in Large N Slightly Broken Higher Spin (SBHS) theories. As an illustration of the methodology, we work out the three point functions which reproduce the previously known results. We then work out the four point functions of spinning operators. We show that the correlation functions of spinning operators in the interacting SBHS theory take a remarkably simple form and that they can be written just in terms of the free fermionic and critical bosonic theory correlators. They also interpolate nicely between the results in these two theories. When expressed in spinor-helicity variables we obtain an anyonic phase which nicely interpolates between the free fermionic and critical bosonic results which makes 3D bosonization manifest. Further, we also obtain a form for five and higher point functions as well by performing a similar analysis.

Prabhav Jain

Bibhut Sahoo

Dhruva K.S.

Aashna Zade

Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to free theory correlators

In this paper, we make connection between CFT$_{3}$ three point correlation function of conserved currents and 4D three point amplitude of general spin massless gauge field explicit. We do so by taking flat space limit of momentum space CFT correlation function and show how they reproduce flat space amplitudes. We then point out a mismatch between number of independent structures in 3D CFT correlator of conserved currents and 4D flat space covariant vertex of massless higher spin fields. This is in contrast with general expectation that counting of 3d CFT correlator and 4d flat space amplitude should match. This mismatch is even more pronounced in spinor helicity variables.We also point out an interesting relation between parity even and parity odd flat space amplitude in momentum space. This observation helps us to construct a new momentum space CFT structure which accounts for the mismatch. However we should mention that this extra CFT structure can't be constructed out of conserved currents and hence counting mismatch between CFT correlation of conserved currents and flat space amplitude of massless gauge field persists. Story in spinor helicity variable is more complicated and is discussed in detail. We further comment on the connection of CFT correlation function in spinor helicity variables to AdS amplitudes in spinor helicity variables and light cone variables.

Abhishek Mehta

4D flat-space scattering amplitude/ Correlator Correspondence Revisited

De-Sitter(dS) space allows for a generalized class of vacua, known as α–vacua, described by some parameters. The Bunch-Davies (BD) vacuum is a point in this parameter space. The cosmological correlation function in BD vacuum in four dimensions and can be interpreted as CFT 3 correlation function of certain operators. However, the correlation function in α–vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in α–vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the α–vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space.

Suman Kundu

Sunil Sake

A CFT interpretation of cosmological correlation functions in α−vacua in de-Sitter space

Using a novel relation between the parity-even and -odd parts of a correlator, we show that the three-point function of conserved or weakly broken currents in three-dimensional conformal field theory (CFT) can be obtained from just the free fermion (FF) or the free boson (FB) theory. In the special case of large <math><mi>N</mi></math> Chern-Simons matter theories, we obtain the correlator in terms of a coupling constant dependent “anyonic phase” factor. This anyonic phase factor was previously obtained in the <math><mn>2</mn><mo>→</mo><mn>2</mn></math> exact S-matrix result and is consistent with strong-weak duality. By varying the coupling constant, the CFT correlator interpolates nicely between the same in the FF and FB theories.