We demonstrate a relation between Nielsen’s approach toward circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating Kähler structures on the full projective Hilbert space of low rank algebras. This geometric structure of the states in the Hilbert space ensures that every unitary transformation of the associated algebras leave the metric and the symplectic forms invariant. We further associate a classical matter free Jackiw-Teitelboim gravity model with these state manifolds and show that the dilaton can be interpreted as the quantum mechanical expectation values of the symmetry generators. On the other hand, we identify the dilaton with the spread complexity over a Krylov basis thereby proposing a geometric perspective connecting two different notions of complexity.

We consider a perturbative expansion of the Lanczos coefficients and the Krylov complexity for two-dimensional conformal field theories under integrable deformations. Specifically, we explore the consequences of $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ , $$ \textrm{J}\overline{\textrm{T}} $$ J T ¯ , and $$ \textrm{J}\overline{\textrm{J}} $$ J J ¯ deformations, focusing on first-order corrections in the deformation parameter. Under $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation, we demonstrate that the Lanczos coefficients b _n exhibit unexpected behavior, deviating from linear growth within the valid perturbative regime. Notably, the Krylov exponent characterizing the rate of exponential growth of complexity surpasses that of the undeformed theory for positive value of deformation parameter, suggesting a potential violation of the conjectured operator growth bound within the realm of perturbative analysis. One may attribute this to the existence of logarithmic branch points along with higher order poles in the autocorrelation function compared to the undeformed case. In contrast to this, both $$ \textrm{J}\overline{\textrm{J}} $$ J J ¯ and $$ \textrm{J}\overline{\textrm{T}} $$ J T ¯ deformations induce no first order correction to either the linear growth of Lanczos coefficients at large-n or the Krylov exponent and hence the results for these two deformations align with those of the undeformed theory.

Classical soft theorems applied to probe scattering processes on AdS₄ spacetimes predict the existence of perturbative 1/L² corrections to the soft photon and soft graviton factors of asymptotically flat spacetimes. In this paper, we establish that the 1/L² corrected soft photon theorem can be derived from a large N CFT₃ Ward identity. We derive a perturbed soft photon mode operator on a flat spacetime patch in global AdS₄ in terms of an integrated expression of the boundary CFT current. Using the same in the CFT₃ Ward identity, we recover the 1/L² corrected soft photon factor derived from classical soft theorems.

The quantum complexity of conformal field theory (CFT) states can be computed holographically from the dual gravitational solutions. In this paper, we have studied the late-time growth of holographic complexity of a charged black hole in five-dimensional anti–de Sitter spacetime in the presence of quartic derivative interaction terms using the $complexity=action$ conjecture. These interaction terms in the gravitational action can lead to the violation of Lloyd’s bound. The dual CFT is known to admit a hydrodynamic description where the KSS bound is also violated due to higher derivative terms in the bulk action. The origin of terms which violate both bounds are the same for the gravitational action of consideration. It is fascinating that the wormhole and the boundary fluid show similar features in the presence of higher derivative terms. We have also discussed the late-time complexity growth rate of the Jackiw-Teitelboim (JT) model with higher derivative corrections.

A bstract: We calculate the logarithmic temperature corrections to the thermodynamic entropy of four-dimensional near-extremal Reissner-Nordström de Sitter (dS) black hole by computing a one-loop contribution within the path integral framework in the near-horizon limit. Due to the presence of three horizons, the extremal limit of a charged dS black hole is fundamentally different from its flat and AdS counterparts. In the near-horizon limit, there are three distinct extremal limits known as cold, Nariai, and ultracold configurations. We compute the tensor zero modes of the Lichnerowicz operator acting on linearized metric perturbations for the cold and Nariai extremal limits which are associated with near-horizon AdS ₂ and dS ₂ asymptotic symmetries. In particular in the near-Nariai limit we compute the quantum corrections to the Hartle-Hawking wavefunction at late times. Our computation establishes the result that at leading order, the small temperature corrections to the extremal entropy is universal in the cold and Nariai limit, paving the way for similar such computations and tests in higher dimensional dS black hole spacetimes, including rotating dS black holes.

The W(a, b) and $$W(a,b;\bar{a},\bar{b})$$W ( a , b ; a ¯ , b ¯ ) algebras are deformations of $$\mathfrak {bms}_{3}$$bms 3 and $$\mathfrak {bms}_{4}$$bms 4 algebras, respectively. We present a $$\mathcal {N}=2$$N = 2 supersymmetric extension of both algebras in the presence of Rsymmetry generators that rotates the two supercharges. Our construction provides the most generic central extensions of the W(a, b) algebra. In particular, we find that $$\mathcal {N}=2$$N = 2 $$\mathfrak {bms}_{3}$$bms 3 algebra admits a new central extension. On the other hand, we explicitly demonstrate that an infinite $$U(1)_V \times U(1)_A$$U ( 1 ) V × U ( 1 ) A extension of the $$W(a,b;\bar{a},\bar{b})$$W ( a , b ; a ¯ , b ¯ ) algebra corresponding to the $$R-$$R - symmetry is not possible for linear and quadratic structure constants with generic deformation parameters. This also implies that the infinite R symmetry considered in our analysis is broken for the $$\mathcal {N}=2 \, \mathfrak {bms}_{4}$$N = 2 bms 4 algebra.