Holographic complexity: braneworld gravity versus the Lloyd bound

We construct Type IIB string theory setups which, via double holography, realize two gravitational systems in separate AdS spaces which interact with each other and with a non-gravitational bath. We employ top-down string theory solutions with concrete field theory duals in the form of 4d $$\mathcal{N}$$ = 4 SYM BCFTs and a first-principles notion of double holography. The setups are used to realize pairs of ‘near’ and ‘far’ black holes from the perspective of the bath, which exchange Hawking radiation with each other and radiate into the bath. We identify three phases for the entropy in the bath characterized as no island, partial island and full island, and discuss the entropy curves. The setups differ from the black hole binaries observed in gravitational wave experiments but may capture certain aspects.

Section: Jhep05(2024)120mentioning

confidence: 99%

Binary AdS black holes coupled to a bath in Type IIB

Deddo,

Zayas,

Uhlemann

2024

Cosmological singularities, holographic complexity and entanglement

Narayan,

Saini,

Yadav

2024

We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with AdS, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.

Krylov complexity of deformed conformal field theories

Chattopadhyay,

Malvimat,

Mitra

2024

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 bn 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.