We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric. Up to normalization, the Krylov complexity of a Hermitian operator then equals the length squared of a straight-line trajectory on the manifold of unitaries that connects the identity operator with a precursor operator. The corresponding length provides an upper bound on Nielsen complexity that saturates whenever the straight line is a minimal geodesic. While for general systems we can only establish saturation in the limit of small precursors, we provide evidence that in the Sachdev-Ye-Kitaev (SYK) model there is a precise correspondence between Krylov complexity and (the square of) Nielsen complexity for a finite range of precursors.

We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with holographic matter, coupled to a pair of holographic CFTs on the asymptotic boundaries. The dimension of the Hilbert space spanned by the microstates of this doubly holographic black hole is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies of the left and right black holes. Importantly, the quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy of the eternal black hole, and thus can be interpreted as quantifying the entanglement between the two asymptotic boundaries.

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of constructing solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace is unchanged, and we observe time evolutions with a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.

We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators (OTOCs) and Krylov complexity. In the EFT, a shift symmetry of the hydrodynamic modes enforces the maximal Lyapunov exponent in OTOCs, $\lambda_L = 2\pi T$, while simultaneously constraining thermal two-point autocorrelators. We solve these constraints on the autocorrelator, and calculate the Lanczos coefficients and Krylov exponents for several examples, finding both $\lambda_K = \lambda_L$ and $\lambda_K = \lambda_L/2$. This demonstrates that, within the EFT, the shift symmetry alone is insufficient to enforce maximal Krylov exponents even when the Lyapunov exponent is maximal. In particular, this result suggests a tension with the conjectured bound $\lambda_L \leq \lambda_K \leq 2\pi T$. Finally, we identify autocorrelator solutions whose power spectra closely resemble the so-called thermal product formula seen in holographic systems.

We study the early Universe evolution of axion-like particle (ALP) domain walls taking into account the effect of friction from particles in the surrounding plasma, including the case of particles in thermal equilibrium and frozen out species. We characterize the friction force from interactions within the ALP effective theory, providing new results for the fermion contribution as well as identifying simple conditions for friction to be relevant during the domain wall life time. When friction dominates, the domain wall network departs from the standard scaling regime and the corresponding gravitational wave emission is affected. As a relevant example, we show how this can be the case for ALP domain walls emitting at the typical frequencies of Pulsar Timing Array experiments, when the ALP couples to the SM leptons. We then move to a general exploration of the gravitational wave prospects in the ALP parameter space. We finally illustrate how the gravitational wave signal from ALP domain walls is correlated with the quality of the underlying $U(1)$ symmetry.

First order phase transitions (FOPT) in the early Universe can be powerful emitters of both relativistic and heavy particles, upon the collision of ultra-relativistic bubble shells. If the particles coupling to the bubble wall have CP-violating interactions, the same collision process can also create a local lepton or baryon charge. This CP-violation can originate from different channels, which have only been partially addressed in the literature. We present a systematic analysis of the different channels inducing CP-violation during bubble collisions: 1) the decay of heavy particles 2) the production of heavy particles and 3) the production of light and relativistic Standard Model (SM) particles. As an illustration of the impact that such mechanisms can have on baryon number and dark matter (DM) abundance, we then introduce a simple model of cogenesis, separating a positive and a negative lepton number in the SM and a dark sector (DS). The lepton number asymmetry in the SM can be used to explain the baryon asymmetry of the Universe (BAU), while the opposite asymmetry in the DS is responsible for determining the abundance of DM. Moreover, the masses of light neutrinos can be understood via the inverse seesaw mechanism, with the lepton-violating Majorana mass originating from the FOPT. A typical smoking gun signal of this class of models is the irreducible gravitational wave (GW) background produced by the PT. We find that a substantial portion of the parameter space can be probed at future observatories like the Einstein Telescope (ET).

We illustrate scenarios in which Hawking radiation collected in finite regions of a reservoir provides temporary access to the interior of black holes through transient entanglement "islands". Whether these islands appear and the amount of time for which they dominate - sometimes giving way to a thermalization transition - is controlled by the amount of radiation we probe. In the first scenario, two reservoirs are coupled to an eternal black hole. The second scenario involves two holographic quantum gravitating systems at different temperatures interacting through a Rindler-like reservoir, which acts as a heat engine maintaining thermal equilibrium. The latter situation, which has an intricate phase structure, describes two eternal black holes radiating into each other through a shared reservoir.

We describe an extension of the FeynRules package dedicated to the automatic generation of the mass spectrum associated with any Lagrangian-based quantum field theory. After introducing a simplified way to implement particle mixings, we present a new class of FeynRules functions allowing both for the analytical computation of all the model mass matrices and for the generation of a C++ package, dubbed ASperGe. This program can then be further employed for a numerical evaluation of the rotation matrices necessary to diagonalize the field basis. We illustrate these features in the context of the Two-Higgs-Doublet Model, the Minimal Left-Right Symmetric Standard Model and the Minimal Supersymmetric Standard Model.

Thermal states holographically dual to black holes in Einstein gravity display maximal Lyapunov growth as well as "butterfly effect cones". We study these effects in highly non-equilibrium states, obtained from an initial thermal state by the sudden injection of energy. We do this by computing out-of-time-order correlators (OTOCs) in BTZ-Vaidya spacetimes, which describe transitions between black holes at different temperatures. If both pairs of boundary operators appearing in the OTOC are inserted before the energy injection, we recover standard results, with butterfly effect cones displaying a light-cone structure. But when one pair of operators is inserted before and the other pair after the energy injection, the Lyapunov growth saturates the chaos bounds set by the local temperatures and the butterfly effect cones "open up", becoming superluminal, albeit in a way that does not violate causality. In the limiting case, in which the initial state is the vacuum, Lyapunov growth only starts after the energy injection. Our computations of the OTOCs are phrased in terms of gravitationally interacting particles, where fields are treated in a geodesic approximation and the eikonal phase shift is expressed in terms of stress tensors and shock waves associated to geodesics.

We use non-Abelian T-duality to construct new N=1 solutions of type IIA supergravity (and their M-theory lifts) that interpolate between AdS_5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way we give an elegant formulation of non-Abelian T-duality when acting on a wide class of backgrounds, including those corresponding to such flows, in terms of their SU(2) structure.

We revisit the electroweak phase transition in the scalar singlet extension of the standard model with a $\mathbb{Z}_2$ symmetry. In significant parts of the parameter space the phase transition occurs in two steps - including canonical benchmarks used in experimental projections for gravitational waves. Domain walls produced in the first step of the transition seed the final step to the electroweak vacuum, an effect which is typically neglected but leads to an exponentially enhanced tunnelling rate. We improve previous results obtained for the seeded transition, which made use of the thin-wall or high temperature approximations, by using the mountain pass algorithm that was recently proposed as a useful tool for seeded processes. We then determine the predictions of the seeded transition for the latent heat, bubble size and characteristic time scale of the transition. Differences compared to homogeneous transitions are most pronounced when there are relatively few domain walls per hubble patch, potentially leading to an enhanced gravitational wave signal. We also provide a derivation of the percolation criteria for a generic seeded transition, which applies to the domain wall seeds we consider as well as to strings and monopoles.

By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find that the key requirement in Harlow-Wu's algorithm fails to be met in the whole covariant phase space. Instead, it can be satisfied in its submanifold with the null boundaries given by the expansion free and shear free hypersurfaces in Einstein's gravity, which can be regarded as the origin of the non-triviality of null boundaries in terms of Wald-Zoupas's prescription. But nevertheless, by sticking to the variational principle as our guiding principle and adapting Harlow-Wu's algorithm to the aforementioned submanifold, we successfully reproduce the Hamiltonians obtained previously by Wald-Zoupas' prescription, where not only are we endowed with the expansion free and shear free null boundary as the natural stand point for the definition of the Hamiltonian in the whole covariant phase space, but also led naturally to the correct boundary term for such a definition.

We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with holographic matter, coupled to a pair of holographic CFTs on the asymptotic boundaries. The dimension of the Hilbert space spanned by the microstates of this doubly holographic black hole is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies of the left and right black holes. Importantly, the quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy of the eternal black hole, and thus can be interpreted as quantifying the entanglement between the two asymptotic boundaries.

Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries. This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes. In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display "slow scrambling", characterized by cubic (rather than exponential) growth. Superposed on this average power-law growth is a sawtooth pattern, whose steep parts correspond to brief periods of Lyapunov growth associated to the nonzero temperature of the right-moving degrees of freedom in a dual conformal field theory. Next we study the extent to which these OTOCs are modified in certain "superstrata", horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region, some of which we evaluate explicitly.

We systematically study model-independent constraints on the three generic charged Higgs couplings to $b$-quarks and up-type quarks. While existing LHC searches have focussed on the $tb$ coupling, we emphasize that the LHC plays a crucial role in probing also $ub$ and $cb$ couplings, since constraints from flavor physics are weak. In particular we propose various new searches that can significantly extend the present reach on the parameter space by: i) looking for light charged Higgses that decay into $ub$-quarks, ii) probing charged Higgs couplings to light and top quarks using multi-$b$-jet signatures, iii) looking for single $b$-quarks in low-mass dijet searches, iv) searching for charge asymmetries induced by charged Higgs production via $ub$ couplings.

We use non-Abelian T-duality to construct new N=1 solutions of type IIA supergravity (and their M-theory lifts) that interpolate between AdS_5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way we give an elegant formulation of non-Abelian T-duality when acting on a wide class of backgrounds, including those corresponding to such flows, in terms of their SU(2) structure.

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate `complexity metric' must be used that takes into account the relative difficulty of performing `nonlocal' operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to ~10^4.

First order phase transitions are violent phenomena that occur when the state of the universe evolves abruptly from one vacuum to another. A \emph{direct} phase transition connects a local vacuum to a deeper vacuum of the zero--temperature potential, and the energy difference between the two minima manifests itself in the acceleration of the bubble wall. In this sense, the transition is triggered by the release of vacuum energy. On the other hand, an \emph{inverse} phase transition connects a deeper minimum of the zero--temperature potential to a higher one, and the bubble actually expands against the vacuum energy. The transition is then triggered purely by thermal corrections. We study for the first time the hydrodynamics and the energy budget of inverse phase transitions. We find several modes of expansion for inverse bubbles, which are related to the known ones for direct transitions by a mirror symmetry. We finally investigate the friction exerted on the bubble wall and comment on the possibility of runaway walls in inverse phase transitions.

In this talk, we present a mechanism of Dark Matter production during first order phase transitions and happening via the collision of the bubble wall and plasma quanta. We will first study the possibility that the dark matter is produced via a renormalisable operator. We will observe that in this context the DM can be much heavier than the scale of the phase transition and has a large initial velocity, leading to the possibility of the DM to be warm today. We will then turn to more realistic scenarios where the Dark Matter sector is secluded and its interaction with the visible sector (including the Standard Model) originates from dimension-five and dimension-six operators. In this regime, we also find that such DM is typically heavy and warm today. We study separately the cases of weakly and strongly coupled dark sectors, where, in the latter case, we focus on glueball DM, which turns out to have very distinct phenomenological properties. For completeness, we also systematically compute the Freeze-In production of the dark sector and compare it with the bubble-plasma DM abundances. All the analytical results are collected in a table presented in this paper.

Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order 1/epsilon^2. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive relations for the coefficients of the time-averaged theory that are likely to be useful for evaluating them more efficiently in numerical simulations.