Entwinement as a possible alternative to complexity

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been identified before.

We study holographic complexity for the rotating quantum BTZ black holes (quBTZ), the BTZ black holes with corrections from bulk quantum fields. Using double holography, the combined system of backreacted rotating BTZ black holes with conformal matters, can be holographically described by the rotating AdS4 C-metric with the BTZ black hole living on a codimension-1 brane. We investigate both volume complexity and action complexity of rotating quBTZ, and pay special attention to their late-time behaviors. When the mass of BTZ black hole is not very small compared to geff2/3/G3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {g}_{\ extrm{eff}}^{2/3}/{G}_3 $$\\end{document} and the rotation is not very slow compared to parameter ℓ, where geff as well as ℓ both characterize the backreaction of quantum fields and G3 is the 3D Newton constant, we show that the late-time rates of the volume complexity and the action complexity agree with each other up to a factor 2 and reduce to the ones of BTZ at the leading classical order, and they both receive subleading quantum corrections. For the volume complexity, the leading quantum correction comes from the backreaction of conformal matter on the geometry, similar to the static quBTZ case. For the action complexity, unlike the static case, the Wheeler-de Witt (WdW) patch in computing the action complexity for the rotating black hole does not touch the black hole singularity such that the leading order result is in good match with the one of classical BTZ. However, when the mass of BTZ black hole is small compared to geff2/3/G3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {g}_{\ extrm{eff}}^{2/3}/{G}_3 $$\\end{document} or the rotation parameter a is small compared to ℓ, the quantum correction to the action complexity could be significant such that the late-time slope of the action complexity of quBTZ deviates very much from the one of classical BTZ. Remarkably, we notice that the nonrotating limit a → 0 is singular and the action complexity of the static quBTZ black holes cannot be reproduced by taking the nonrotating limit a → 0 on the one of the rotating black holes. This discontinuity also appears in higher dimensional rotating black holes, such as Kerr-AdS4 black hole and rotating AdS5 black hole.

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle’s mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that ‘gravity is the weakest force’. Here, we take a step towards making this expectation more precise by studying ℤN and ℤ2N gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to MPl.

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested using test particles and fields. It has been claimed that such a black hole can be overspun. In this paper, we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes using the scattering of a scalar field. The first law of thermodynamics in the non-extremal BTZ black hole is recovered. For the extremal and near-extremal black holes, due to the divergence of the variation of entropy, we test the weak cosmic censorship conjecture by evaluating the minimum of the function f, and find that both the extremal and near-extremal black holes cannot be overspun.

In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the BTZ black holes. Even though BTZ black holes without any angular momentum or electric charge thermodynamically behave as an ideal gas, i.e. with non-interacting microstructures; in the presence of electric charge or angular momentum, BTZ black holes are associated with repulsive interactions among the microstructures. We extend the study to the case of exotic BTZ black holes with mass $M = \alpha m + \gamma \frac{j}{l}$ and angular momentum $J=\alpha j + \gamma l m$, for arbitrary values of $ (\alpha, \gamma)$ ranging from purely exotic $(\alpha=0,\gamma=1)$, slightly exotic $(\alpha > \frac{1}{2},\gamma < \frac{1}{2})$ and highly exotic $(\alpha < \frac{1}{2}, \gamma > \frac{1}{2})$. We find that unlike the normal BTZ black holes (the case $\alpha =1,\gamma =0$), there exist both attraction as well as repulsion dominated regions in all the cases of exotic BTZ black holes.

In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state is a corresponding quotient of the CFT vacuum state. This state turns out to live in the aforementioned product CFT. We discuss this result in the context of general issues of AdS/CFT duality and entanglement entropy.

If the inflaton couples to other degrees of freedom that populate the post-inflationary stage, such coupling modifies the dynamics of the inflaton \emph{during} inflation. We consider light fermions Yukawa coupled to the inflaton as "unobserved" degrees of freedom integrated out of the total density matrix. Tracing out these degrees of freedom yields a \emph{mixed} density matrix whose time evolution is described by an effective field theory. We show that the coupling leads to profuse fermion pair production for super-Hubble inflaton fluctuations which lead to the \emph{growth of entanglement entropy during inflation}. The power spectrum of inflaton fluctuations features scale invariance violations $\mathcal{P}(k) = \mathcal{P}_0(k)\,\,\exp\{8\,\xi_k\}$ with corrections to the \emph{index and its running directly correlated with the entanglement entropy}: $S_{vN} = - \sum_{k} \Big[ \ln(1-\xi_k) + \frac{\xi_k\,\ln(\xi_k)}{1-\xi_k} \Big]$. For super-Hubble fluctuations we find $\xi_k = -\frac{Y^2}{48\pi^2}\Big\{2\,N_T\,\ln(k/k_f) + \ln^2(k/k_f)\Big\}$ with $Y$ the Yukawa coupling, $N_T$ the total number of e-folds during inflation, and $k_f$ a "pivot" scale corresponding to the mode that crosses the Hubble radius at the end of inflation.

By applying the island rule proposed recently, we compute the entanglement entropy of Hawking radiation and study the Page curve for the eternal black holes in massive gravity. We investigate for both the neutral and charged black holes which the corresponding results of Schwarzschild and Reissner–Nordström black holes are restored in the limit of massless graviton. We show for the neutral and non-extremal charged black holes that the island is not formed at the early times of the evaporation and hence the entanglement entropy increases linearly in time. However, for the extremal charged black hole, the calculation of the entanglement entropy at the early times without the island is ill-defined because the metric is divergent at the curvature singularity. This implies that new physics in the UV region must be taken into account to make the metric behaving smoothly at the very short distances. At the late times, with the emergence of one island near the event horizon, the entanglement entropy is saturated by the Bekenstein–Hawking entropy of black holes. In addition, we analyze the impact of massive gravity parameters on the size of island, the entanglement entropy, the Page time, and the scrambling time in detail.

Discrete gauge symmetries in axionic extensions of the supersymmetric standard model

We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group {mathbb{Z}}_n . Such models are obtained by studying first a specific toric set-up whose associated Heterotic vector bundle has structure group {mathbb{Z}}_n . By employing a conjectured Heterotic/F-theory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compactifications to six dimensions. We provide explicit constructions of mirror-pairs for symmetric examples with {mathbb{Z}}_2 and {mathbb{Z}}_3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in field theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stückelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections.

We know that criteria for thermodynamic stability of a most general black hole appears in the form of a series of inequalities connecting second-order derivatives of the black hole mass with respect to its parameters. Quasi-stable black holes satisfy some of these stability criteria in a certain regime of parameter space, but they never satisfy all the criteria simultaneously. We also know that specific heat, by virtue of our general stability criteria, is not necessarily negative for quasi-stable black holes. We show here that ([Formula: see text])-dimensional charged super entropic BTZ black hole is thermodynamically quasi-stable if fluctuation in cosmological constant is taken into account. We in fact study the fluctuations of all the thermodynamic parameters of this black hole in detail, namely, its charge, horizon area and cosmological constant. This detailed study concludes that this BTZ black hole transforms into some other kind of black hole during its Hawking decay and becomes stable. We also show differences in thermodynamic properties between this charged super entropic BTZ black hole and other AdS black holes.

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system's energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum's uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity.

We calculate log corrections to the entropy of three-dimensional black holes with “soft hairy” boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories with anisotropic scaling of Lifshitz type with dynamical exponent z at the boundary. On the gravity side such scalings arise for KdV-type boundary conditions, which provide a specific 1-parameter family of multi-trace deformations of the usual AdS3/CFT2 setup, with Brown-Henneaux corresponding to z = 1 and soft hairy boundary conditions to the limiting case z → 0+. Both approaches agree in the case of BTZ black holes for any non-negative z. Finally, for soft hairy boundary conditions we show that not only the leading term, but also the log corrections to the entropy of black flowers endowed with affine û (1) soft hair charges exclusively depend on the zero modes and hence coincide with the ones for BTZ black holes.

We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker \\rough" version of the conjecture is respected. We calculate the renormalized energymomentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.

The thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli black hole endowed with Korteweg--de Vries (KdV)-type boundary conditions are reconsidered. This family of boundary conditions is labeled by a non-negative integer $n$, and gives rise to a dual theory which possesses anisotropic Lifshitz scaling invariance with dynamical exponent $z=2n+1$. We show that from the scale invariance of the action for stationary and circularly symmetric spacetimes, an anisotropic version of the Smarr relation arises. Finally, we analyze the global and local thermal stability of the system and we found that the specific heat of the black hole is positive for all possible values of $z$, and at the self-dual temperature ${T}_{s}=\frac{1}{2\ensuremath{\pi}}(\frac{1}{z}{)}^{\frac{z}{z+1}}$, there is a Hawking-Page phase transition between the BTZ black hole and thermal ${\mathrm{AdS}}_{3}$ spacetime.