## Final Report Summary - SPLE (String Phenomenology in the LHC Era)

Our main objectives in the SPLE project have been to

1) Improve our understanding of String Theory solutions describing the structure of the Standard Model(SM) of Particle Physics

2) Study the implications of the Large Hadron Collider results for string theory. Let us only mention here some of the highlights.

1) We have computed for the first time detailed Yukawa couplings within the context of F-theory SU(5) Grand Unification. This required the study of a new theoretical tool, T-branes, which play a fundamental role in the computation of U-quark Yukawas. We find that one can numerically describe the quark/lepton masses and mixings within this theory. A second important direction in which we have obtained important results is the construction of large field models of cosmological Inflation from String Theory. We have introduced a new class of string inflation models termed ’’F-term axion monodromy inflation’’, which has been widely studied since then. We have also shown that Type II String Theory solutions posses built-in discrete shift symmetries which guarantee the stability of large field inflation models and constructed the first string theory examples of a ''Nilpotent Goldstino'', useful in other classes of inflation models. The study of those so called monodromy models has lead us to discover an interesting built-in structure in Type II compactifications. The effective potential may always be written in terms of a quadratic form which explicitly displays all the network of discrete shift symmetries of the theory. We have shown that this structure is extremely useful to study the minima and symmetries of a given compactification.

2) Implications of the LHC results. The message of the LHC seems to be that some degree of fine-tuning in the Higgs sector is necessary. If Supersymmetry exists, it must be at scales relatively large or very large. This negative result gives though important information. We have found that if SUSY is broken at a very high scale, intermediate between the Electro-Weak and the Planck scales, unification arguments predict a mass for the Higgs close to 126 +- 3 GeV, in agreement with experiment. In such a scheme the Higgs field of the Supersymmetric Standard Model can also act as a cosmological inflaton, giving rise to a new version of chaotic inflation termed "Higgsotic inflation". On the other hand, with heavy or no supersymmetry, the hierarchy problem requires fine-tuning or some sort of other alternative. One of them, in which the Higgs field takes a small value because of dynamical cosmological reasons, is the "relaxion" idea. We have constructed for the first time relaxion models with monodromy symmetries protecting the relaxion from uncontrolled gravitational corrections. We have also studied models in which the SM Higgs scans in a "landscape" of possible masses.

In these new developments we have found that the idea of the "swampland" of theories turns out to be very important. The swampland is the set of effective field theories which cannot be embedded into a consistent theory of quantum gravity. In the last three years it has been realized that there are important general swampland constraints both on cosmology and Particle Physics. Our group has taken a leading role in these developments. We first pointed out how the Weak Gravity Conjecture (WGC) swampland arguments strongly constraint and even rule out large classes of trans-Planckian axion moderls of inflation. We have also shown strong constraints on models of "relaxions" and "clockwork". Finally we have also shown how certain extensions of the Weak Gravity Conjecture applied directly to the SM gives rise to important constraints which relate the masses of neutrinos to the cosmological constant and new avenues for the understanding of the fine-tuning of the Higgs.

1) Improve our understanding of String Theory solutions describing the structure of the Standard Model(SM) of Particle Physics

2) Study the implications of the Large Hadron Collider results for string theory. Let us only mention here some of the highlights.

1) We have computed for the first time detailed Yukawa couplings within the context of F-theory SU(5) Grand Unification. This required the study of a new theoretical tool, T-branes, which play a fundamental role in the computation of U-quark Yukawas. We find that one can numerically describe the quark/lepton masses and mixings within this theory. A second important direction in which we have obtained important results is the construction of large field models of cosmological Inflation from String Theory. We have introduced a new class of string inflation models termed ’’F-term axion monodromy inflation’’, which has been widely studied since then. We have also shown that Type II String Theory solutions posses built-in discrete shift symmetries which guarantee the stability of large field inflation models and constructed the first string theory examples of a ''Nilpotent Goldstino'', useful in other classes of inflation models. The study of those so called monodromy models has lead us to discover an interesting built-in structure in Type II compactifications. The effective potential may always be written in terms of a quadratic form which explicitly displays all the network of discrete shift symmetries of the theory. We have shown that this structure is extremely useful to study the minima and symmetries of a given compactification.

2) Implications of the LHC results. The message of the LHC seems to be that some degree of fine-tuning in the Higgs sector is necessary. If Supersymmetry exists, it must be at scales relatively large or very large. This negative result gives though important information. We have found that if SUSY is broken at a very high scale, intermediate between the Electro-Weak and the Planck scales, unification arguments predict a mass for the Higgs close to 126 +- 3 GeV, in agreement with experiment. In such a scheme the Higgs field of the Supersymmetric Standard Model can also act as a cosmological inflaton, giving rise to a new version of chaotic inflation termed "Higgsotic inflation". On the other hand, with heavy or no supersymmetry, the hierarchy problem requires fine-tuning or some sort of other alternative. One of them, in which the Higgs field takes a small value because of dynamical cosmological reasons, is the "relaxion" idea. We have constructed for the first time relaxion models with monodromy symmetries protecting the relaxion from uncontrolled gravitational corrections. We have also studied models in which the SM Higgs scans in a "landscape" of possible masses.

In these new developments we have found that the idea of the "swampland" of theories turns out to be very important. The swampland is the set of effective field theories which cannot be embedded into a consistent theory of quantum gravity. In the last three years it has been realized that there are important general swampland constraints both on cosmology and Particle Physics. Our group has taken a leading role in these developments. We first pointed out how the Weak Gravity Conjecture (WGC) swampland arguments strongly constraint and even rule out large classes of trans-Planckian axion moderls of inflation. We have also shown strong constraints on models of "relaxions" and "clockwork". Finally we have also shown how certain extensions of the Weak Gravity Conjecture applied directly to the SM gives rise to important constraints which relate the masses of neutrinos to the cosmological constant and new avenues for the understanding of the fine-tuning of the Higgs.