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## Proposals for Master or PhD thesis at LPTHE

### Applications of supergravity and string theory to High-energy physics

*Advisor: Ignatios Antoniadis*

High-energy physics enters a new era with the Large Hadron Collider (LHC) at CERNsearching for new particles and forces at energies ten times bigger than previously, creating conditions similar to those of the early Universe, just after the Big Bang. At the same time, several new observations arise from experiments in astrophysics and cosmology, which complete our understanding of the same physics, while the direct and indirect search of dark matter continues. There is a real opportunity to extract the underlying microscopic theory, beyond the current standard models of particle physics and cosmology. The subject of this thesis is to explore several theoretical ideas and proposals, based on supersymmetry, string theory, extra dimensions and holography, in order to make progress in this direction. Indeed, supersymmetry is space-time symmetry motivated by theoretical arguments and experimental indications. On the other hand, string theory renders compatible two fundamental theories: quantum mechanics and general relativity, by replacing the notion of point particles by extended objects. Two important consequences are the existence of extra dimensions and the possible brane-world description of our Universe.

Several research directions are possible. Central questions are: (i) the origin of the different scales associated with a theory describing cosmology, gravitation and particle physics; (ii) the role of supersymmetry at a fundamental level and its possible non- linear realisation at low energies. Possible research objectives are: (1) Particle physics and cosmology of (approximate) de Sitter vacua in supergravity, towards the description of both inflation and present dark energy. (2) Non-linear supersymmetry and cosmology. (3) In the context of string theory, compactification methods, mechanisms of supersymmetry breaking, the structure of the effective supergravity and its properties, the computation of non-perturbative effects, the propagation of strings in curved spacetime, and the study of gravitational phenomena in regions of strong curvature where the effective field theory approach breaks down.

The expected duration of the thesis is three years. During the first months, the candidate should rather study the literature in this highly competitive subject, in order to improve her/his level and to be able to choose the precise research direction depending on personal interests.

A Master internship is possible, prior to the start of the PhD thesis.

### Gravitational waves and BSM physics

*Advisor: Karim Benakli*

Gravitational waves detected on earth might have been produced a long time ago and have traveled a long way through space. Therefore they provide a new mean for the observation of the early universe, along with electromagnetic radiations. The spectrum of gravitational waves depends both on the production mechanism and on the content of the universe it crossed. The subject of this thesis is to continue the investigation of the form and kind of information on physics beyond the Standard Model of particle physics that can be obtained from detection of gravitational waves at different wavelengths.

### Effect of quenched disorder on the order-by-disorder transition in frustrated magnets

*Advisor: Leticia Cugliandolo, Co-advisor: Marco Tarzia (LPTMC)*

Many interesting classical and quantum magnets are highly constrained. In particular, geometric constraints imply frustration and the impossibility of satisfying all competing interactions simultaneously, leading to highly degenerate ground states [1].

Geometric frustration can lead to a rich variety of unusual behaviors. A remarkable example is the Order by Disorder (OBD) transition, i.e., the mechanism whereby a system with non- trivially degenerate ground states lifts the degeneracy and develops long-range order by the effect of classical or quantum fluctuations. From a theoretical point of view, the OBD mechanism is a relatively common occurrence in systems such as the fully frustrated domino model introduced by Villain, or the Ising antiferromagnet on the three-dimensional FCC lattice. Many other theoretical realizations exist. Nevertheless, conclusive evidence for thermal OBD remains unseen in the laboratory so far. The difficulty lies in establishing whether order is selected through the OBD mechanism (a huge disproportion in the density of low-energy excitations associated with particular ground states) or is due to energetic contributions not taken into account that actually lift the ground-state degeneracy.

In Ref. [2] we demonstrated thermal ODB in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. Our analysis elucidates the mechanism whereby a symmetry-broken state is selected by thermal excitations, and establishes a route to the much-sought-after experimental realization of classical ODB, both in two-dimensional artificial systems, or in antiferromagnetic all-in-all-out pyrochlores.

However, real samples are affected by impurities, defects, and imperfections which may lift the ground-state degeneracy explicitly. It is therefore important to study the effects of such quenched disorder on the ODB transition. This is precisely the aim of this research proposal. More specifically, we will focus on the 2d fully frustrated domino model in presence of different types of randomness, in the limit of low temperature and weak disorder.

At low enough temperatures the thermodynamical properties should be determinired by the low-energy excitations. The analysis leads to an effective one dimensional model, in which macro-spins interact via effective couplings that depend on the temperature and the linear size of the system. This model can then be solved exactly with the transfer matrix approach even in the presence of quenched disorder. We plan to check the analytical results with extensive Monte Carlo simulations of large systems. The effects of the quenched disorder on the anomalous finite-size effects associated to the OBD transition should be investigated as well.

[1] https://en.wikipedia.org/wiki/Geometrical_frustration

[2] P. Guruciaga, M. Tarzia, M. V. Ferreyra, L. F. Cugliandolo, S. A. Grigera, and R. A. Borzi, *Field-tuned order-by-disorder in frustrated magnets with antiferromagnetic interactions*, arXiv:1606.02972 Phys. Rev. Lett. 117, 167203 (2016).

### Non-perturbative effects in dark matter and baryogenesis

*Advisor: Kalliopi Petraki*

Dark matter and the matter-antimatter asymmetry of the universe are two of the most important pieces of evidence for the existence of unknown fundamental physics. As the experimental constraints for new physics below the TeV scale become more stringent, a new interest in the exploration of the multi-TeV regime has emerged. In many such scenarios, dark matter is assumed to interact via force mediators that are much lighter than itself. The resulting long-range interactions give rise to non-perturbative effects, such as the existence of bound states, which can affect the phenomenology of dark matter in a variety of ways. Similar dynamics may be at play in the processes responsible for the generation of the matter-antimatter asymmetry of the universe. In fact, these two open problems may be related. The project will explore particle physics models that feature this kind of dynamics, and will entail model- building aspects, as well as cosmological and astrophysical phenomenology.

### Pushing the precision frontier of LHC physics: Automating QCD resummation for new physics

*Advisor: Benjamin Fuks, Co-advisor: Hua-Sheng Shao*

The Standard Model of particle physics is an extremely successful theory, with (almost) all observations performed so far perfectly matching the predictions. However, the present experimental status also reveals several of the conceptual issues and practical limitations of the Standard Model, like the absence of a candidate for dark matter or the hierarchy problem. The Standard Model is therefore acknowledged as an effective theory that should originate from a more fundamental one yet to be discovered, and new phenomena are expected at energies well below the Planck scale. Whilst there are currently numerous intriguing features that provide hints that new physics could be accessible at energies that are already probed, none of these are yet significant enough to exclude the standard paradigm. However, as more data is being collected, we have reason to be optimistic towards the close future.

One interesting avenue in the searches for new physics relies on indirect probes in which precision theoretical predictions are confronted to accurate experimental measurements. The state-of-the-art for new physics predictions for the LHC consists in Monte Carlo simulations in which matrix elements including the next-to-leading order corrections driven by quantum chromodynamics (QCD) are matched with parton showers. While the accuracy of parton shower is quite limited so far, QCD resummation procedure provides a systematic way to improve it. In more details, fixed-order QCD perturbative computations are only justified when the perturbative series is controlled by a small expansion parameter. Close to the production threshold or when QCD emission are soft and/or collinear, large logarithmic terms need to be resummed. Whilst such a resummation can be handled through parton showers, its accuracy is limited so that analytical computations are in order to provide a better description at the hard-scattering level.

This thesis fits within this context and aims to automate perturbative QCD resummation calculations for various observables relevant for the LHC, both in the framework of the Standard Model and for new physics. The planned research will extend two existing programs developed at the LPTHE and that are widely used in the high-energy physics community, namely MADGRAPH5_aMC@NLO [1] and RESUMMINO [2]. Whilst we plan to start studying standard candles (total rates, invariant mass and transverse-momentum distributions of one or more final state particles) in the Standard Model, phenomenological applications to new physics will be conducted later on. We indeed plan to focus both on well-motivated ultraviolet-complete models (such as models featuring a strong dynamics at a high-energy scale or supersymmetric models) and effective field theories extending the Standard Model by higher-dimensional operators.

The technical part of the project consists in understanding how next-to-leading order calculations in QCD work and in devising an efficient method to extract the components allowing for performing all-order QCD resummation. Whilst a first training on the Standard Model and supersymmetry for which analytical results exist will be achieved, generalisation to any process from any theory will be foreseen in a second step. The deliverable consists in the building of a plugin linking MADGRAPH5_aMC@NLO and RESUMMINO, so that any physicist could compute precision predictions for any model. Moreover, tables of total and differential cross sections relevant for LHC and future collider physics will be provided, as this is known as relevant inputs for the high-energy physics community.

Within this project, the candidate is expected to develop a deep knowledge of new physics models and phenomenology, as well as acquire strong computing skills in QCD. Achieving the predefined goals will allow the candidate to obtain a strong expertise both in the development and in the usage of various tools widely used in our community, which is a valuable expertise for most research groups in the world.

[1] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.S. Shao, T. Stelzer, P. Torrielli and M. Zaro, *The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations*, JHEP 1407 (2014) 079.

[2] B. Fuks, M. Klasen, D.R. Lamprea and M. Rothering, *Precision predictions for electroweak superpartner production at hadron colliders with Resummino*, Eur. Phys. J. C 73 (2013) 2480.

### Perturbative and non-perturbative aspects of three-dimensional gauge-field theories

*Advisor: Sofian Teber*

One of the most fascinating and challenging problems of theoretical physics is the understanding of the origin of the mass of particles. Historically, according to the textbook [1], it is probably Landau, Abrikosov and Khlatnikov who first suggested that a fermion mass may be dynamically generated in quantum gauge-field theories; in their 1956 paper [2], they wrote: “it can evidently be supposed that... the mass of an electron is of wholly electromagnetic origin”; they also recognized that such a phenomenon is beyond the reach of simple perturbation theory. Interestingly, it is within the field of condensed matter physics that the first example of a theory displaying dynamical symmetry breaking (DSB) was given: the Bardeen-Cooper-Schrieffer theory of superconductivity (1957) whereby a gap in the fermion spectrum is dynamically generated due to fermion pairing. Soon after (1960), Nambu realized that the particle physics counterpart of this phenomenon was the dynamical generation of a fermion mass. Since then, there has been extensive theoretical work carried out to understand DSB both in non-relativistic and relativistic models. To this day, the understanding of such complicated phenomena in even-, e.g., (3 + 1)-, dimensional gauge field theories such as QED4 and QCD4 is still incomplete.

In the 80s, the study of simpler models, such as QED in (2 + 1)-dimensions or QED3, was advocated by Pisarski [3]. Since then, this model has attracted considerable attention because it shares many features with QCD4 (asymptotic freedom and confinement). A salient feature of the model is that it displays dynamical chiral (or flavour) symmetry breaking when the number of fermion flavours, N, is below a critical value, Nc; for N < Nc a dynamical mass is generated. Of interest is, for example, to compute the precise value of Nc [4]. Recently, this has become a very hot topic again attracting the attention of physicists from different communities (from condensed matter physics to string theory), see, e.g., [5, 6, 7, 8]. One of the most robust prediction is based on a recent analytic solution of next-to-leading order (1/N2) Schwinger-Dyson equations, see [9] for a review. This is a promising field-theoretic achievement opening the way to further important developments with respect to variants of QED3 and, eventually, to higher dimensional models where many challenging problems remain to be solved.

The subject of the PhD thesis will be devoted to the field theoretic study of (strongly coupled) three-dimensional gauge-field theories. The central issues are to explore the perturbative structure of three-dimensional gauge theories which is more subtle and less well-known than the one of four-dimensional models; and to apply/develop methods consisting of using the perturbative data as an input to understand non-perturbative features of the model. Applications will be related (but not limited to) to condensed matter physics of planar systems. Familiarity with advanced multi-loop techniques is not required and proper training on these techniques will be given. The interested applicant should however have a basic knowledge of relativistic quantum field theory, e.g., at the level of ICFP Theoretical Physics Master 2 and, preferably, good programming skills (C, Python).

The expected duration of the PhD thesis is three years. A Master 2 internship on the subject is also possible before starting the thesis.

Key words: quantum field theory, three-dimensional models, renormalization group, radiative corrections, Feynman diagrams, multi-loop calculations, Schwinger-Dyson equations, large-N approximation, dynamical mass generation, planar condensed matter physics systems.

References

[1] V. A. Miransky, *Dynamical symmetry breaking in quantum field theories*, Singapore, Singapore: World Scientific (1993).

[2] L. D. Landau, A. Abrikosov and I. M. Khalatnikov, *On the quantum theory of fields*, Nuovo Cimento 3 80 (1956).

[3] R. D. Pisarski, *Chiral Symmetry Breaking in Three-Dimensional Electrodynamics*, Phys. Rev. D 29 (1984) 2423.

[4] T. Appelquist, D. Nash and L. C. R. Wijewardhana, *Critical Behavior in (2+1)-Dimensional QED*, Phys. Rev. Lett. 60 (1988) 2575

[5] S. Giombi, G. Tarnopolsky and I. R. Klebanov, *On CJ and CT in Conformal QED*, JHEP 1608 (2016) 156

[6] I. F. Herbut, *Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation*, Phys. Rev. D 94 (2016) 025036

[7] V. P. Gusynin and P. K. Pyatkovskiy, *On the critical number of fermions in three-dimensional QED*, arXiv:1607.08582 [hep-ph]

[8] A. V. Kotikov and S. Teber, *Critical behaviour of (2 + 1)-dimensional QED: 1/Nf-corrections in an arbitrary non-local gauge*, arXiv:1609.06912 [hep-th]

[9] S. Teber, *Field theoretic study of electron-electron interaction effects in Dirac liquids*, arXiv:1810.08428 [cond-mat.mes-hall].