Supersymmetric Field Theories and Isomonodromic Deformations

The topic of this thesis is the recently discovered correspondence between supersymmetric gauge theories, two-dimensional conformal field theories and isomonodromic deformation problems. Its original results are organized in two parts: the first one, based on the papers [1], [2], as well as on some further unpublished results, provides the extension of the correspondence between four-dimensional class S theories and isomonodromic deformation problems to Riemann Surfaces of genus greater than zero. The second part, based on the results of [3], is instead devoted to the study of five-dimensional superconformal field theories, and their relation with q-deformed isomonodromic problems

BPS Spectra and Algebraic Solutions of Discrete Integrable Systems

This paper extends the correspondence between discrete Cluster Integrable Systems and BPS spectra of five-dimensional $\mathcal{N}=1$ QFTs on $\mathbb{R}^4\times S^1$ by proving that algebraic solutions of the integrable systems are exact solutions for the system of TBA equations arising from the BPS spectral problem. This statement is exemplified in the case of M-theory compactifications on local del Pezzo Calabi-Yau threefolds, corresponding to q-Painlev\'e equations and $SU(2)$ gauge theories with matter. A degeneration scheme is introduced, allowing to obtain closed-form expression for the BPS spectrum also in systems without algebraic solutions. By studying the example of local del Pezzo 3, it is shown that when the region in moduli space associated to an algebraic solution is a ``wall of marginal stability'', the BPS spectrum contains states of arbitrarily high spin, and corresponds to a 5d uplift of a four-dimensional nonlagrangian theory.Comment: 38 pages, 11 figure

The threefold way to quantum periods: WKB, TBA equations and q-Painlev\'e

We show that TBA equations defined by the BPS spectrum of $5d$ $\mathcal{N}=1$ $SU(2)$ Yang-Mills on $S^1\times \mathbb{R}^4$ encode the q-Painlev\'e III$_3$ equation. We find a fine-tuned stratum in the physical moduli space of the theory where solutions to TBA equations can be obtained exactly, and verify that they agree with the algebraic solutions to q-Painlev\'e. Switching from the physical moduli space to that of stability conditions, we identify a one-parameter deformation of the fine-tuned stratum, where the general solution of the q-Painlev\'e equation in terms of dual instanton partition functions continues to provide explicit TBA solutions. Motivated by these observations, we propose a further extensions of the range of validity of this correspondence, under a suitable identification of moduli. As further checks of our proposal, we study the behavior of exact WKB quantum periods for the quantum curve of local $\mathbb{P}^1\times\mathbb{P}^1$.Comment: 39 Pages + 2 Appendices, 10 Figure

From interacting spin-2 fields to multimetric supergravities

In this thesis we take the first steps on the road that goes from studying nonlinear interactions between spin-2 fields to investigating those between spin-2 supermultiplets. After the recent discovery of the nonlinear theory of massive gravity by de Rham, Gabadadze and Tolley and its subsequent generalization to multimetric theories of gravity, in which we see nonlinear interactions between multiple massive spin-2 fields and a single massless one, much progress has been done in the understanding of these theories, which admit two formulations: one exploits metric tensors, while the other employs vielbein variables. The latter formulation in particular allows to avoid the square root tensor apparently unavoidable in the metric approach. Originally, the main motivation for the study of these theories was that they seem to naturally exhibit self-acceleration, and thus to have the potential to address the issue of dark energy. Recently it has been suggested that the additional spin-2 field may also be an interesting dark matter candidate. The main result of this thesis is to provide the supersymmetric extension of multimetric gravities in the vielbein formulation for space-time dimensions up to D = 4. These classes of supergravity models were not explored so far. Apart from their intrinsic interest, multimetric supergravities may be relevant for a number of reasons. For instance, they may shed light on the positive energy branch of the non supersymmetric theory, in the same way as the proof of the positive energy theorem for General Relativity was greatly simplified by Witten, using results coming from Supergravity. Further, taking into account the presence of massive supermultiplets, there may be room for the implementation of new types of supersymmetry breaking scenarios. In the present work we focused on the general construction, leaving to future investigation the analysis of possible applications. Due to the particular form of the interaction potential, usual superfield techniques could not be straightforwardly applied to the case at hand. For this reason, in order to tackle the problem we resorted to recent developments on the theory of integration over supermanifolds, generalizations of the usual differentiable manifolds to the case in which anticommuting (fermionic) coordinates are considered. In particular, we made systematic use of the calculus of integral forms: if one considers ordinary differential forms as polynomials of the differentials (with multiplication given by the wedge product), integral forms will be instead distributions in the same variables with support in the origin. This approach has the advantage of allowing to describe integration on supermanifolds using forms in a very similar way as in the usual case, and thus to write manifestly supercovariant actions. We were able, using this tool, to write the actions which generalize the multimetric gravity models by displaying manifest local supersymmetry. We observed that multimetric gravity theories incarnate particular instances of a more general mechanism that gives mass to gauge fields. We implemented this mechanism both in the Yang-Mills case and in the case of a supersymmetric spin-1 multiplet: for the latter, interestingly enough, we could see explicitly how the multiplets recombine in the right way giving full massive multiplets together with a single massless one. Also, the massless and massive combinations are the same in this case and in gravity, again showing the generality of the underlying mechanism. While our description holds at the classical level, it would be interesting to study the quantum theory of the vector case. Our work on these new supersymmetric theories, both in the spin-1 and in the spin-2 case, led to the article "Multimetric Supergravities" (arXiv:1605.06793 [hep-th]). We also investigated some aspects of multimetric theories in the non-supersymmetric context. Indeed, one of conceptual conundrums of multimetric gravity is that the underlying geometry maybe is not yet fully transparent. In this thesis we tried to shed some additional light in this respect: we generalized a covariant constraint analysis made by Deser et al. for the case of dRGT massive gravity to that of bimetric gravity, in which we have one diffeomorphism and one local Lorentz invariance. This allowed us to give a clear direct interpretation in terms of gauge symmetries of some of the constraints arising from the equations of motion. With this information we were able to give a group manifold formulation of bimetric gravity: in this type of treatment, one sees the fibre bundle structure of the theory, which is usually taken as the starting point, emerging from its field equations. This allows to see clearly that the geometric structure underlying bimetric gravity is exactly the same as that of General Relativity: a “Poincaré bundle” in which the diffeomorphisms can be interpreted as a “gauging” of the translation sector of the Poincaré group. An interesting perspective would be to see if one can interpret the limitations to the possible interaction terms one can consider in the case of more than two vielbeins in light of these new results. In addition, we also tried to develop an alternative view on the geometry of the vielbein formulation. In particular, we proposed a new set of variables providing a nonlinear extension of the linear massless mode of bimetric gravity. In our opinion this nonlinear extension looks more natural than those previously considered in the context of the metric formulation. Further, in these new variables, for a specific choice of the parameters, it appears that the action of bimetric gravity in the metric formulation may be rewritten without any square-root tensor

Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus

We compute the monodromy dependence of the isomonodromic tau function on a torus with $n$ Fuchsian singularities and $SL(N)$ residue matrices by using its explicit Fredholm determinant representation. We show that the exterior logarithmic derivative of the tau function defines a closed one-form on the space of monodromies and times, and identify it with the generating function of the monodromy symplectomorphism. As an illustrative example, we discuss the simplest case of the one-punctured torus in detail. Finally, we show that previous results obtained in the genus zero case can be recovered in a straightforward manner using the techniques presented here.Comment: 24 pages, 3 figure

Terahertz rectifyier for integrated image detector

We present a new CMOS compatible direct conversion terahertz detector operating at room temperature. The rectenna consists in a truncated conical helix extruded from a planar spiral and connected to a nanometric metallic whisker at one of its edges. The whisker reaches the semiconductor substrate that constitutes the antenna ground plane. The rectifying device can be obtained introducing some simple modifications of the charge storage well in conventional CMOS APS devices, making the proposed solution easy to integrate with existing imaging systems. No need of scaling toward very scaled and costly technological node is required, since the CMOS only provides the necessary integrated readout electronics. On-wafer measurements of RF characteristics of the designed rectifying junction are reported and discussed

CMOS-Compatible Room-Temperature Rectifier Toward Terahertz Radiation Detection

In this paper, we present a new rectifying device, compatible with the technology of CMOS image sensors, suitable for implementing a direct-conversion detector operating at room temperature for operation at up to terahertz frequencies. The rectifying device can be obtained by introducing some simple modifications of the charge-storage well in conventional CMOS integrated circuits, making the proposed solution easy to integrate with the existing imaging systems. The rectifying device is combined with the different elements of the detector, composed of a 3D high-performance antenna and a charge-storage well. In particular, its position just below the edge of the 3D antenna takes maximum advantage of the high electric field concentrated by the antenna itself. In addition, the proposed structure ensures the integrity of the charge-storage well of the detector. In the structure, it is not necessary to use very scaled and costly technological nodes, since the CMOS transistor only provides the necessary integrated readout electronics. On-wafer measurements of RF characteristics of the designed junction are reported and discussed. The overall performances of the entire detector in terms of noise equivalent power (NEP) are evaluated by combining low-frequency measurements of the rectifier with numerical simulations of the 3D antenna and the semiconductor structure at 1 THz, allowing prediction of the achievable NEP

Numerical insights on ionic microgels: structure and swelling behaviour

Recent progress has been made in the numerical modelling of neutral microgel particles with a realistic, disordered structure. In this work we extend this approach to the case of co-polymerised microgels where a thermoresponsive polymer is mixed with acidic groups. We compare the cases where counterions directly interact with microgel charges or are modelled implicitly through a Debye-H\"uckel description. We do so by performing extensive numerical simulations of single microgels across the volume phase transition (VPT) varying the temperature and the fraction of charged monomers. We find that the presence of charges considerably alters the microgel structure, quantified by the monomer density profiles and by the form factors of the microgels, particularly close to the VPT. We observe significant deviations between the implicit and explicit models, with the latter comparing more favourably to available experiments. In particular, we observe a shift of the VPT temperature to larger values as the amount of charged monomers increases. We also find that below the VPT the microgel-counterion complex is almost neutral, while it develops a net charge above the VPT. Interestingly, under these conditions the collapsed microgel still retains a large amount of counterions inside its structure. Since these interesting features cannot be captured by the implicit model, our results show that it is crucial to explicitly include the counterions in order to realistically model ionic thermoresponsive microgels