We compute the Krylov Complexity of a light operator $$ \mathcal{O} $$O _L in an eigenstate of a 2d CFT at large central charge c. The eigenstate corresponds to a primary operator $$ \mathcal{O} $$O _H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of $$ \mathcal{O} $$O _H is below or above the critical dimension h_H = c/24, marked by the 1st order Hawking-Page phase transition point in the dual AdS₃ geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d, and in the integrable 2d Ising CFT, where there is no such transition in the spectrum of states.

In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five-point function of the scalar operator in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques can be easily generalised to momentum space correlators of complicated spinning operators and to higher point functions. The three dimensional fermionic theory has the interesting feature that the scalar operator $$ \overline{\psi}\psi $$ψ ¯ ψ is odd under parity. To account for this, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of $$ \overline{\psi}\psi $$ψ ¯ ψ operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use them to solve for three-point functions involving spinning operators without invoking conformal invariance. However, at the level of four-point functions, solving the HS equation requires additional constraints that come from conformal invariance and we could only verify that our explicit results solve the HS equation.

In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories. The direct Feynman diagram approach to computing correlation functions is intricate and in general has been performed only in specific kinematic regimes. We use higher spin equations to obtain the parity even and parity odd contributions to two-, three- and four-point correlators involving spinning and scalar operators in a general kinematic regime, and match our results with existing results in the literature for cases where they are available.One of the interesting facts about higher spin equations is that one can use them away from the conformal fixed point. We illustrate this by considering mass deformed free boson theory and solving for two-point functions of spinning operators using higher spin equations.

We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in [equation] dimensional conformal field theories ([equation])...

We establish the large central charge behavior of the entanglement negativity for a mixed state configuration of a single interval enclosed between two intervals in a holographic ${\mathrm{CFT}}_{1+1}$. To this end we utilize the monodromy technique to elucidate the large central charge limit of a four point twist correlator which characterizes the negativity of the mixed state configuration. Subsequently we analyze the large central charge limit of the six point twist correlator which reduces to the above four point correlator in a specific limit. The results provide a strong consistency check for our recently proposed holographic entanglement negativity conjecture in the ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ scenario.

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in [equation] dimensional conformal field theories ([equation])...