## Final Report Summary - STRINGPHENOATLHC (String Phenomenology at the Era of LHC)

Light stringy states :

Plan

The analysis of light stringy states relies heavily on conformal field theory techniques. They will determine various highly non-trivial correlators containing (higher) excited bosonic twist field correlators. With their knowledge they study the production and decays of stringy states via computing string scattering amplitudes.

The decays will be studied in details with the aid of Monte Carlo methods. At this stage of the project, interaction with the experimental group at DESY, which is involved in the ATLAS project at CERN, is expected. Their expertise and experience will provide the most authoritative comparison of such signals and LHC data. Their result in comparison with data will provide hints towards the very interesting question whether we live in a low string scale scenario.

Achievements

Robert Richter in collaboration with P. Anastosopoulos performed a detailed analysis of the scattering amplitude containing light stringy states. Here they relied heavily on an earlier work, where they computed various correlators containing the usual bosonic twist correlators as well as excited bosonic twist fields. Given the results of the string scattering amplitudes they establish experimental signatures of those light stringy states which can be tested at LHC. This resulted in a publication, that has been published in JHEP.

As a follow up project, in collaboration with P. Anastasopoulos and M. Bianchi they intensify those studies, including also higher spin fields. Again they plan to establish their experimental signatures which can be tested at LHC, but moreover we plan to investigate the couplings of higher spin fields to other string states (see below). They plan to publish their results in the forthcoming months.

Higher spin states :

Plan

The derivation of higher order Higher spin field interactions within string compactifications using conformal field theory techniques.

Achievements

As already mentioned above Robert Richter currently works in collaboration with P. Anastasopoulos and M. Bianchi on establishing those interaction. This analysis strongly relies on the previous published work on twist field correlators performed by R. Richter, P. Ansastsopoulos and M. Goodsell. They plan to publish their results in the forthcoming months.

Discrete symmetries and D-instantons:

Plan

It will be required a first, preliminary period of study of Calabi-Yau manifolds with respect to their isometries. A large amount of algebraic and differential geometry will be needed improving the knowledge and techniques of the applicant.

Once a classification of Calabi-Yau manifolds with promising isometries is given the plan is to move forward and construct realistic D-brane configurations within such compactification manifolds. Afterwards Robert Richter plans to study the discrete symmetries of those constructions with respect to their phenomenological implications, with emphasis on the Yukawa textures.

The above results will be added in the algorithm in order to scan by a computer for vacua with interesting phenomenological features.

Achievements

Here Robert Richter changed slightly the focus, by analysing rather abelian discrete symmetries that originate from global U(1) symmetries.

In a project, in collaboration with P. Anastasopoulos and B. Schellekens, Robert Richter investigated the presence of abelian discrete symmetries in the context of semi-realistic globally consistent Gepner models. In an earlier work other authors found that abelian discrete symmetries are rather rarely realised in those constructions. More importantly, in their systematic search they could not find any MSSM-like models in which Baryon triality can be realised. Robert Richter and his collaborators generalise their search by allowing the discrete symmetry to partially originate form the hidden sector. Allowing for this generalisation they find that discrete symmetries are rather typical in Gepner models and, moreover, they find that some specific constructions exhibit Baryon triality, thus they give a natural explanation for the absence of dimension 5 proton decay operators. This resulted in a publication, that has been published in JHEP.

In a follow up project they extend their search to other Gepner constructions, investigating whether they can find also the discrete symmetries matter parity and proton triality. Moreover, they want to identify what features a Gepner construction has to satisfy in order to give a specific type of discrete symmetry. Here they observe that by simple explorative data analysis they cannot find a dictionary between features of a Gepner model and the type of discrete symmetry. Thus recently Robert Richter attended various workshops to learn more advanced computer techniques, such as machine learning algorithm, that may help to reveal such a dictionary. Robert Richter plans to publish results related to this study in the first half of 2016.

Moduli stabilization and de Sitter vacuum:

Plan

The search for de Sitter vacua in the context of toroidal compactification requires a careful analysis of the scalar potential for the moduli fields. Various contributions, such as flux contributions, non-perturbative superpotential contributions, perturbative Kahler corrections, may be important and their exact size needs to be determined. After the computation of all moduli dependent contributions to the scalar potential, the plan is to search for metastable de Sitter vacua.

Achievements

Robert Richter in collaboration with Jan Louis analysed the scalar potential of toroidal orbifold constructions. Unfortunately, in the study not any stable minima leading to a positive cosmological constant has been found.

D-brane model building / D-instantons:

Plan

To establish a set of criteria that will be embedded in a large scale computerised search for realistic string vacua.

Achievements

Robert Richter, in collaboration with Jan Louis initiated an investigation of phenomenological aspects of typical semi-realistic type II/ F-theory constructions. Specifically, they study the general patterns of SUSY-breaking soft terms that arise in typical type II SUSY-breaking scenarios. The plan is to determine some typical, however model independent signatures, that are potentially observable at the next run of LHC. However, they realised that this goal was a bit of too ambitious, since sightly different string compactifications can lead to significant different observations.

Therefore they rather focused on determining a dictionary between features of a string compactifications and their phenomenological implications. For this study an exploratory analysis of the data is not sufficient, but one rather needs advanced machine learning algorithms (for big data). Thus Robert Richter attended various workshops and seminars intensify his knowledge about these techniques. Equipped with those techniques the plan is to publish some interesting results in the forthcoming months.

Vacuum energy sequestering:

Plan

This was not plan of the original proposal.

Achievements

Recently, Kaloper and Padilla proposed a mechanism to sequester the standard model vacuum contributions to the cosmological constant. Robert Richter in collobration with I. Ben-Dayan, F. Ruehle, and A. Westphal studied the consequences of embedding their proposal into a fully local quantum field theory. They find that the resulting Lagrangian is that of a spontaneously broken conformal field theory, indicating that there proposal has some underlying conformal field theory structure. The results of this work has been submitted to JCAP.

Plan

The analysis of light stringy states relies heavily on conformal field theory techniques. They will determine various highly non-trivial correlators containing (higher) excited bosonic twist field correlators. With their knowledge they study the production and decays of stringy states via computing string scattering amplitudes.

The decays will be studied in details with the aid of Monte Carlo methods. At this stage of the project, interaction with the experimental group at DESY, which is involved in the ATLAS project at CERN, is expected. Their expertise and experience will provide the most authoritative comparison of such signals and LHC data. Their result in comparison with data will provide hints towards the very interesting question whether we live in a low string scale scenario.

Achievements

Robert Richter in collaboration with P. Anastosopoulos performed a detailed analysis of the scattering amplitude containing light stringy states. Here they relied heavily on an earlier work, where they computed various correlators containing the usual bosonic twist correlators as well as excited bosonic twist fields. Given the results of the string scattering amplitudes they establish experimental signatures of those light stringy states which can be tested at LHC. This resulted in a publication, that has been published in JHEP.

As a follow up project, in collaboration with P. Anastasopoulos and M. Bianchi they intensify those studies, including also higher spin fields. Again they plan to establish their experimental signatures which can be tested at LHC, but moreover we plan to investigate the couplings of higher spin fields to other string states (see below). They plan to publish their results in the forthcoming months.

Higher spin states :

Plan

The derivation of higher order Higher spin field interactions within string compactifications using conformal field theory techniques.

Achievements

As already mentioned above Robert Richter currently works in collaboration with P. Anastasopoulos and M. Bianchi on establishing those interaction. This analysis strongly relies on the previous published work on twist field correlators performed by R. Richter, P. Ansastsopoulos and M. Goodsell. They plan to publish their results in the forthcoming months.

Discrete symmetries and D-instantons:

Plan

It will be required a first, preliminary period of study of Calabi-Yau manifolds with respect to their isometries. A large amount of algebraic and differential geometry will be needed improving the knowledge and techniques of the applicant.

Once a classification of Calabi-Yau manifolds with promising isometries is given the plan is to move forward and construct realistic D-brane configurations within such compactification manifolds. Afterwards Robert Richter plans to study the discrete symmetries of those constructions with respect to their phenomenological implications, with emphasis on the Yukawa textures.

The above results will be added in the algorithm in order to scan by a computer for vacua with interesting phenomenological features.

Achievements

Here Robert Richter changed slightly the focus, by analysing rather abelian discrete symmetries that originate from global U(1) symmetries.

In a project, in collaboration with P. Anastasopoulos and B. Schellekens, Robert Richter investigated the presence of abelian discrete symmetries in the context of semi-realistic globally consistent Gepner models. In an earlier work other authors found that abelian discrete symmetries are rather rarely realised in those constructions. More importantly, in their systematic search they could not find any MSSM-like models in which Baryon triality can be realised. Robert Richter and his collaborators generalise their search by allowing the discrete symmetry to partially originate form the hidden sector. Allowing for this generalisation they find that discrete symmetries are rather typical in Gepner models and, moreover, they find that some specific constructions exhibit Baryon triality, thus they give a natural explanation for the absence of dimension 5 proton decay operators. This resulted in a publication, that has been published in JHEP.

In a follow up project they extend their search to other Gepner constructions, investigating whether they can find also the discrete symmetries matter parity and proton triality. Moreover, they want to identify what features a Gepner construction has to satisfy in order to give a specific type of discrete symmetry. Here they observe that by simple explorative data analysis they cannot find a dictionary between features of a Gepner model and the type of discrete symmetry. Thus recently Robert Richter attended various workshops to learn more advanced computer techniques, such as machine learning algorithm, that may help to reveal such a dictionary. Robert Richter plans to publish results related to this study in the first half of 2016.

Moduli stabilization and de Sitter vacuum:

Plan

The search for de Sitter vacua in the context of toroidal compactification requires a careful analysis of the scalar potential for the moduli fields. Various contributions, such as flux contributions, non-perturbative superpotential contributions, perturbative Kahler corrections, may be important and their exact size needs to be determined. After the computation of all moduli dependent contributions to the scalar potential, the plan is to search for metastable de Sitter vacua.

Achievements

Robert Richter in collaboration with Jan Louis analysed the scalar potential of toroidal orbifold constructions. Unfortunately, in the study not any stable minima leading to a positive cosmological constant has been found.

D-brane model building / D-instantons:

Plan

To establish a set of criteria that will be embedded in a large scale computerised search for realistic string vacua.

Achievements

Robert Richter, in collaboration with Jan Louis initiated an investigation of phenomenological aspects of typical semi-realistic type II/ F-theory constructions. Specifically, they study the general patterns of SUSY-breaking soft terms that arise in typical type II SUSY-breaking scenarios. The plan is to determine some typical, however model independent signatures, that are potentially observable at the next run of LHC. However, they realised that this goal was a bit of too ambitious, since sightly different string compactifications can lead to significant different observations.

Therefore they rather focused on determining a dictionary between features of a string compactifications and their phenomenological implications. For this study an exploratory analysis of the data is not sufficient, but one rather needs advanced machine learning algorithms (for big data). Thus Robert Richter attended various workshops and seminars intensify his knowledge about these techniques. Equipped with those techniques the plan is to publish some interesting results in the forthcoming months.

Vacuum energy sequestering:

Plan

This was not plan of the original proposal.

Achievements

Recently, Kaloper and Padilla proposed a mechanism to sequester the standard model vacuum contributions to the cosmological constant. Robert Richter in collobration with I. Ben-Dayan, F. Ruehle, and A. Westphal studied the consequences of embedding their proposal into a fully local quantum field theory. They find that the resulting Lagrangian is that of a spontaneously broken conformal field theory, indicating that there proposal has some underlying conformal field theory structure. The results of this work has been submitted to JCAP.