Non-Abelian orbifolds in string theory

Two dimensional conformal field theories (CFT) play a key role in String theory, in particular they provide a suitable description of dynamics of the string in a given space-time. In this thesis we study 2D conformal theories constructed through toroidal orbifold techniques and arising from superstring compactification on some singular limit of a Calabi-Yau manifold. Orbifolds are one of the main techniques used to construct new two dimensional conformal field theories from known ones. They are obtained by first projecting the CFT on the subsector inva-riant under some finite group of symmetries. In order to obtain a consistent new theory, one is then forced to introduce new sectors (twisted) whose analysis represent the most subtle part of the orbifold construction. In this thesis, we consider orbifolds of the form T 4/G, where T 4 is a four-dimensional torus and G is a finite non-abelian group of discrete symmetries which do not admit a geometric de-scription as isometries of T 4. Torus orbifolds T 4/G may be interpreted as singular limits of Calabi-Yau manifolds of complex dimension two (K3 surfaces). K3 surfaces are the simplest cases of Calabi-Yau manifolds: strings compactifications on K3 have been the background for the first microscopic description in string theory of the Bekenstein-Hawking formula for Black Hole entropy; they are also the framework for one of the most important examples of holographic duality in the AdS/CFT correspondence. Despite these results, generic K3 string models are difficult to describe explicitly: orbifolds T 4/G are some of the few examples where exact computations can be performed. The goal of the thesis is to analyze the main proprieties of orbifolds T 4/G, such as the spectrum, the currents algebra and boundary states, using CFT methods that do not rely on the geometri-cal action of the group G. These methods are then applied to provide the first explicit description of certain examples of T 4/G orbifolds where the group G is non-abelian and/or non-geometric. In particular, we performed explicitly the computation for the group G = 2.A5.ope

Small Black Hole Explosions

Small black holes are a powerful tool to explore infinite distances in moduli spaces. However, we show that in 4d theories with a scalar potential growing fast enough at infinity, it is energetically too costly for scalars to diverge at the core, and the small black hole puffs up into a regular black hole, or follows a runaway behaviour. We derive a critical exponent characterizing the occurrence or not of such small black hole explosions, both from a 4d perspective, and in the 2d theory after an $\bf{S}^2$ truncation. The latter setup allows a unified discussion of fluxes, domain walls and black holes, solving an apparent puzzle in the expression of their potentials in the 4d $\cal{N}=2$ gauged supergravity context. We discuss the realization of these ideas in 4d $\cal{N}=2$ gauged supergravities. Along the way we show that many regular black hole supergravity solutions in the literature in the latter context are incomplete, due to Freed-Witten anomalies (or duals thereof), and require the emission of strings by the black hole. From the 2d perspective, small black hole solutions correspond to dynamical cobordisms, with the core describing an end of the world brane. Small black hole explosions represent obstructions to completing the dynamical cobordism. We study the implications for the Cobordism Distance Conjecture, which states that in any theory there should exist dynamical cobordisms accessing all possible infinite distance limits in scalar field space. The realization of this principle using small black holes leads to non-trivial constraints on the 4d scalar potential of any consistent theory; in the 4d $\cal{N}=2$ context, they allow to recover from a purely bottom-up perspective, several non-trivial properties of vector moduli spaces near infinity familiar from CY$_3$ compactifications.Comment: 40 pages + appendice

Dynamical Cobordism and the beginning of time: supercritical strings and tachyon condensation

We describe timelike linear dilaton backgrounds of supercritical string theories as time-dependent Dynamical Cobordisms in string theory, with their spacelike singularity as a boundary defining the beginning of time. We propose and provide compelling evidence that its microscopic interpretation corresponds to a region of (a strong coupling version of) closed tachyon condensation. We argue that this beginning of time is closely related to (and shares the same scaling behaviour as) the bubbles of nothing obtained in a weakly coupled background with lightlike tachyon condensation. As an intermediate result, we also provide the description of the latter as lightlike Dynamical CobordismThis work is supported through the grants CEX2020-001007-S and PGC2018- 095976-B-C21, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. The work by R.A. is supported by the grant BESST-VACUA of CSIC. The work by M.D. is supported by the FPI gran no. FPI SEV-2016-0597-19-3 from Spanish National Research Agency from the Ministry of Science and Innovatio

At the end of the world: Local dynamical cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world ‘branes’. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric USp(32) theory, Bubbles of Nothing, 4d N = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraintsThis work is supported through the grants CEX2020-001007-S and PGC2018-095976-B-C21, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. The work by R.A. is supported by the grant BESST-VACUA of CSIC. The work by M.D. is supported by the FPI gran no. FPI SEV-2016-0597-19-3 from Spanish National Research Agency from the Ministry of Science and Innovation. The work by J.C. and J. H. is supported by the FPU grants no. FPU17/04181 and FPU20/01495 from the Spanish Ministry of Educatio

Catecholamine-induced Takotsubo syndrome: a case series

Background: Catecholamine-induced Takotsubo Syndrome (cat-TS) is a type of secondary Takotsubo syndrome, characterized by rapid onset of symptoms, high rate of complications during the acute phase, good short-term prognosis, and frequent apical sparing at echocardiogram. We present two clinical cases of cat-TS treated in our department. Case summary: Case one: 78-year-old man, admitted to Ear Nose and Throat Unit for surgical removal of oral squamous cellular carcinoma. During surgery, the occurrence of hypotensive episode was treated with catecholamines. After surgery, the occurrence of atrial fibrillation was followed by evidence of phasic increase of troponin levels and akinesia of midventricular segments. Angiography showed the absence of significant coronary stenoses, and during hospital stay, we observed rapid recovery of wall motion abnormalities. Case two: 64-year-old woman, admitted for hysteropexy surgery, during which cardiac arrest occurred, treated with epinephrine i.v.1 mg and DC shock. Two hours after resuscitation, the patient developed pulmonary oedema, troponin levels increased progressively, and the echocardiogram demonstrated hypokinesia in all midventricular segments with apical sparing. Afterwards, an urgent angiography highlighted normal coronary anatomy. Cardiac magnetic resonance imaging (MRI) revealed oedema corresponding to hypokinetic areas. On the seventh day, echocardiogram showed a complete remission of wall motion abnormalities. Discussion: These cases warn the physicians about the importance of routinely screening myocardial impairment through clinical assessment, electrocardiogram (ECG) monitoring, and serial cardiac troponin testing after catecholamine i.v. bolus administration. In case of alterations of these exams, performing a prompt echocardiogram allows early detection of cat-TS, to provide immediate suitable medical support and avoid complications

Non-Abelian orbifolds in string theory

Two dimensional conformal field theories (CFT) play a key role in String theory, in particular they provide a suitable description of dynamics of the string in a given space-time. In this thesis we study 2D conformal theories constructed through toroidal orbifold techniques and arising from superstring compactification on some singular limit of a Calabi-Yau manifold. Orbifolds are one of the main techniques used to construct new two dimensional conformal field theories from known ones. They are obtained by first projecting the CFT on the subsector inva-riant under some finite group of symmetries. In order to obtain a consistent new theory, one is then forced to introduce new sectors (twisted) whose analysis represent the most subtle part of the orbifold construction. In this thesis, we consider orbifolds of the form T 4/G, where T 4 is a four-dimensional torus and G is a finite non-abelian group of discrete symmetries which do not admit a geometric de-scription as isometries of T 4. Torus orbifolds T 4/G may be interpreted as singular limits of Calabi-Yau manifolds of complex dimension two (K3 surfaces). K3 surfaces are the simplest cases of Calabi-Yau manifolds: strings compactifications on K3 have been the background for the first microscopic description in string theory of the Bekenstein-Hawking formula for Black Hole entropy; they are also the framework for one of the most important examples of holographic duality in the AdS/CFT correspondence. Despite these results, generic K3 string models are difficult to describe explicitly: orbifolds T 4/G are some of the few examples where exact computations can be performed. The goal of the thesis is to analyze the main proprieties of orbifolds T 4/G, such as the spectrum, the currents algebra and boundary states, using CFT methods that do not rely on the geometri-cal action of the group G. These methods are then applied to provide the first explicit description of certain examples of T 4/G orbifolds where the group G is non-abelian and/or non-geometric. In particular, we performed explicitly the computation for the group G = 2.A5

At the End of the World: Local Dynamical Cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world "branes". The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric $USp(32)$ theory, Bubbles of Nothing, 4d $\mathcal{N}=1$ cosmic string solutions, the Klebanov-Strassler throat, D$p$-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.Comment: 42 pages + appendice

Approximate analysis of biological systems by hybrid switching jump diffusion

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations, while the other uses a diffusion process. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation, namely when the process reaches the boundary with non-negligible probability. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation