Moduli Stabilisation and the Holographic Swampland

We investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, and both perturbative and racetrack stabilisation. Interestingly, the LVS vacuum (with $\Delta_{\varphi} = 8.038$) also appears to live very close to a critical value ($\Delta_{\varphi} = 8$) where the anomalous dimensions change sign. We finally point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions.Comment: 37 pages + references, 4 figures; v2 added references and corrected typo

Catch-Me-If-You-Can: The Overshoot Problem and the Weak/Inflation Hierarchy

We study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). LVS cosmology features a long kination epoch as the volume modulus rolls down the exponential slope towards the final minimum, with an energy density that scales as $m_s^4$. This roll admits attractor tracker solutions, and if these are located the overshoot problem is solved. We show that, provided a sufficiently large hierarchy exists between the inflationary scale and the weak scale, this will always occur in LVS as initial seed radiation grows into the tracker solution. The consistency requirement of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales -- an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins, both universal and model-dependent, of the initial seed radiation (or matter). One particularly interesting case is that of a fundamental string network arising from brane inflation -- this may lead to an early epoch in which the universe energy density principally consists of gravitational waves, while an LVS fundamental string network survives into the present universe.Comment: Corrected typos, reference added. Included a comment on the scaling of the total energy density during kinatio

Composite Dark Matter from Strongly-Interacting Chiral Dynamics

A class of chiral gauge theories is studied with accidentally-stable pseudo Nambu-Goldstone bosons playing the role of dark matter (DM). The gauge group contains a vector-like dark color factor that confines at energies larger than the electroweak scale, and a ${\rm U}(1)_D$ factor that remains weakly coupled and is spontaneously broken. All new scales are generated dynamically, including the DM mass, and the IR dynamics is fully calculable. We analyze minimal models of this kind with dark fermions transforming as non-trivial vector-like representations of the Standard Model (SM) gauge group. In realistic models, the DM candidate is a SM singlet and comes along with charged partners that can be discovered at high-energy colliders. The phenomenology of the lowest-lying new states is thus characterized by correlated predictions for astrophysical observations and laboratory experiments.Comment: 56 pages (43 + appendices), 13 figures. v2: minor changes, matching to the published version. One reference added and typos fixe

Composite Dark Matter from Strongly Interacting Chiral Dynamics

The nature of dark matter, whose existence has been inferred indirectly from a large variety of astrophysical and cosmological observations, is arguably one of the greatest mysteries in fundamental physics today. So far, many alternatives have been suggested as a possible solution, ranging from modified theories of gravity to beyond the Standard Model physics or primordial black holes, but unfortunately none of them has received any compelling empirical justification. Amongst them, particle dark matter seems particularly well motivated from a theoretical point of view, since it could also help to shed some light on the open issues in the Standard Model, such as the strong CP problem, grand unification or supersymmetry. An intriguing proposal is that dark matter may be realized as a composite state of a strongly interacting dynamics, coming from a non abelian gauge theory which confines in the infrared. This idea is particularly appealing, since it can account for many of the properties of dark matter in a conceptually economical way, mimicking some already well-known mechanisms in particle physics. For example, adopting an effective field theory point of view, we see that neglecting the non-renormalizable interactions at low energies can enforce some accidental symmetries in our description, which may naturally give rise to the stability of the lightest particle in each multiplet. This is exactly what happens in the Standard Model for baryon number, forbidding proton decay. Since all of these theories do not aim to address electroweak symmetry breaking and related issues, an important fact to keep in mind is that the dark condensation must not break the Standard Model gauge group, and this is what distinguishes them, for example, from Technicolor or Composite Higgs. Up to now, most of the work has focused on Vector-like Confinement 1 scenarios, which were first considered in the context of LHC Phenomenology [1] and later applied to dark matter model building. Their structure provides significant simplifications with respect to the general case, since anomaly cancellation constraints are trivially satisfied and the real representation 2 enables one to conjecture the existence of a global symmetry breaking pattern in the dark sector [2] which preserves the electroweak group. In [3], all possible models consistent with a SU (5) unification of SM gauge forces have been classified, showing 1 A model is called Vector-like if, for any set of fields transforming under a certain represention of the gauge group, a corresponding set of fields transforming under the conjugate representation is also present (or alternatively, the model can be constructed out of Dirac fermions only) 2 at least in the absence of Yukawa couplings 1 that many of them are compatible with current bounds and may exhibit characteristic detection signatures. It is then relevant to ask if the same framework can be successfully applied to chiral models, and whether new phenomenological features can be obtained this way. By chiral we mean that the new fermions transform in a complex representation of the gauge group, with the immediate effect that mass terms are forbidden by gauge invariance. This hypothesis appears to possess some elegant features, and to emerge naturally in the context of physics beyond the Standard Model: • Since mass terms for the dark fermions are not allowed, there is no need for any new, artificial scale. The only relevant one is generated dynamically through dimensional transmutation, and it is what determines the spectrum of the composite states. • Chiral theories play an important role in our understanding of particle physics, with the Standard Model itself being the most obvious example. • If the Standard Model interactions unify in a single gauge group at high energies, the resulting theory must be chiral. The prototypical GUT is the famous SU(5) [4], where each generation of SM matter fields is embedded into a ̄5 and a 10. While it is certainly possible to add vector-like fermions transforming in fragments of chiral GUT representations, one must then introduce an additional mechanism to explain why the other members of the multiplets have acquired a much higher mass. This is analogous to the doublet-triplet splitting problem of Grand Unified Theories (See [5] for a review). For these reasons, chiral models are often thought to be more fundamental; an instructive example can be found in the vector-like QED-QCD system, which finds the explanation of its structure and mass scales in a chiral UV completion, the SM. Chiral models 3 have been considered in [6, 7], where the possibility of a dark, non-anomalous U(1) spontaneously broken by a Higgs mechanism is examined, and also in the context of the mirror world scenario [8]. In addition, some algorithmic methods to construct chiral, anomaly-free extensions of the Standard Model have been devised in [9, 10]. An interesting example was recently considered in [11, 12], where the authors introduced a composite chiral model with four dark fermions charged under the gauge group SU(N ) DC ⊗ U (1) D 4 . The theory confines in the infrared, breaking U (1) D spontaneously (thus giving the dark photon a mass) and forming dark pions and dark baryons, which are bound states exactly analogous to those of QCD. Due to the existence of a global, accidental U (1) V symmetry in the renormalizable lagrangian, the two dark pions are stable and provide a viable dark matter candidate. Interactions with the Standard Model are solely achieved by means of a mixing between the dark and the standard photon [13], which is expected to happen on quite general grounds. The purpose of the thesis is to search for possible extensions of this framework, and examine their phenomenological implications. A possible generalization involves the assignement of charges under the SM gauge groups, adding new portals between the dark sector and SM; this could potentially be very relevant for collider experiments, and also for 3 4 But not necessarily composite D and DC stand for dark and dark colour respectively 2direct detection. In fact, there are no previous examples of a composite chiral model where the dark constituents are not singlets with respect to the SM. More specifically, we identify a new scenario in which the dark fermions also transform as representations of SU(2) L , resulting in a non trivial dark sector characterized by a rich and distinctive phenomenology. Since the model exhibits an approximate SU(4) L ⊗ SU(4) R ⊗ U(1) B symmetry (spontaneously broken to SU(4) V ⊗ U(1) B ), the low energy spectrum of the theory contains 15 Pseudo Nambu-Goldstone bosons (NGBs), one of which is eaten by the dark photon due to the spontaneous breaking of U(1) D induced by condensation in the dark sector. In addition to the U (1) V symmetry described above, which is still present, we point out the existence of a discrete symmetry analogous to charge conjugation, C D , with important implications for processes involving a dark photon. The model satisifies all the necessary requirements to provide viable dark matter candidates: • The cancellation of gauge anomalies is still guaranteed • Landau poles below the GUT scale are avoided for a reasonable range in the choices of the dark charge e D and the number of dark colours N DC • The symmetry breaking pattern is under control, preserving the weak gauge group SU(2) L • A calculation of the pion effective potential shows that the explicit breaking induced by the gauge interactions is sufficient for each of them to obtain a mass, which can be calculated under the assumption of QCD-like sum rules. We write down an appropriate chiral lagrangian for the dark pions containing all the interactions between themselves and with the gauge bosons, thus making the model very predictive. An inspection of these interactions enables one to conclude that only the lightest states with U(1) V charge different from zero are stable and electromagnetically neutral, and to analyze all the decay channels in detail. Since the dark matter candidates are singlets of the electroweak group, interactions with the SM are very suppressed and there are no relevant prospects for direct detection. However, the situation changes dramatically at the collider, where SU(2)-charged NGBs 5 can be efficiently produced through Drell-Yan processes and then decay partially to SM particles. Many of the experimental signatures 6 are similar to those of supersymmetry, and pre-existing searches are used to derive stringent bounds on the mass of the electroweak triplets after calculating their production cross section at LHC. As regards Cosmology and Astrophysics, we derive constraints assuming the correct relic abundance is obtained through a standard thermal freeze-out proceeding via the annihilation channel DM DM → γ D γ D (1) and examine the possible bounds coming from indirect detection. The main result consists in a characterization of the viable parameter space for this class of models, 5 6 Triplets in particular There are, however, some important differences even at the qualitative level 3obtained through a combination of theoretical constraints, cosmological observations and collider data. In particular, we find that only a closed triangle region 7 in the m s − e D plane is allowed, where m s is the dark matter candidate mass (proportional to the dark color condensation scale Λ DC ) and e D the dark charge. This makes the model very predictive, and fully testable in future collider experiments. However, our analysis also leaves a certain number of open questions and future directions to explore. A first possibility is to investigate whether a refinement of our collider bounds may give sensibly different constraints on the model, excluding some or all of the cases. This could be achieved with a more accurate (NLO) computation of the triplet production cross section, and by calculating the precise shape of the kinematic distributions (e.g. in missing energy) to compare with experiment. On the other hand, a more long-term goal is to provide a systematic classification of chiral models, along the lines of what has already been carried out in the case of real representations [3]. References [1] C. Kilic, T. Okui and R. Sundrum: Vectorlike Confinement at the LHC. JHEP 02 (2010) 018. ArXiv: 0906.0577. [2] M. E. Peskin: The Alignment of the Vacuum in Theories of Technicolor. Nucl. Phys. B175 (1980) 197–233 (1980). [3] O. Antipin, M. Redi, A. Strumia and E. Vigiani: Accidental Composite Dark Matter. JHEP 07 (2015) 039. ArXiv: 1503.08749. [4] H. Georgi and S. L. Glashow: Unity of All Elementary Particle Forces. Phys. Rev. Lett. 32 (1974) 438–441 (1974). [5] L. Randall and C. Csaki: The Doublet - triplet splitting problem and Higgses as pseudoGoldstone bosons. In Supersymmetry and unification of fundamental interactions. Proceedings, International Workshop, SUSY 95, Palaiseau, France, May 15-19, 1995 (1995) (pp. 99–109). http://arxiv. org/abs/hep-ph/9508208. [,235(1995)]. [6] A. de Gouvˆea and D. Hern ́andez: New Chiral Fermions, a New Gauge Interaction, Dirac Neutrinos, and Dark Matter. JHEP 10 (2015) 046. ArXiv: 1507.00916. [7] E. Dudas, Y. Mambrini, S. Pokorski and A. Romagnoni: (In)visible Z-prime and dark matter. JHEP 08 (2009) 014. ArXiv: 0904.1745. [8] R. Barbieri, T. Gregoire and L. J. Hall: Mirror world at the large hadron collider . ArXiv: hep-ph/0509242. 7 Only assuming our NGB dark matter candidate does not overclose the universe (i.e. allowing for other particles, such as baryons, to give subdominant contributions to Ω DM ). If, on the other hand, we require the NGBs to reproduce the whole relic density the allowed region becomes a finite curve. 4[9] P. Batra, B. A. Dobrescu and D. Spivak: Anomaly-free sets of fermions. J. Math. Phys. 47 (2006) 082301. ArXiv: hep-ph/0510181. [10] J. M. Berryman, A. de Gouvˆea, D. Hern ́andez and K. J. Kelly: Imperfect mirror copies of the standard model. Phys. Rev. D94(3) (2016) 035009. ArXiv: 1605.03610. [11] K. Harigaya and Y. Nomura: Light Chiral Dark Sector. Phys. Rev. D94(3) (2016) 035013. ArXiv: 1603.03430. [12] R. T. Co, K. Harigaya and Y. Nomura: Chiral Dark Sector. Phys. Rev. Lett. 118(10) (2017) 101801. ArXiv: 1610.03848. [13] B. Holdom: Two U(1)’s and Epsilon Charge Shifts. Phys. Lett. 166B (1986) 196–198 (1986)

The holographic swampland and other topics in string phenomenology

The main topic of this thesis is to explore the consistency and structure of realistic, 4d vacua of String Theory through the AdS/CFT correspondence. As a first step, we investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, the type IIA DGKT flux vacua and both perturbative and racetrack stabilisation. We also point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions. A second, unexpected consequence of this analysis is that the CFT data for some of these vacua takes a universal form, independent of the compactification details. For the type IIA examples, we then give a concise argument that supersymmetric AdS DGKT flux vacua on general Calabi-Yaus always have integer conformal dimensions for all low-lying scalar primaries in the dual CFT. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. We give a tentative discussion of the origin of these integers and effects that would modify these results. In the last part of the thesis, we take a more phenomenological approach and study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). We show that in LVS, provided the existence of a large hierarchy between the inflationary and the weak scales, initial seed radiation will localize the system onto a tracker solution where the problem is solved. The consistency require- ment of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales – an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins (both universal and model- dependent) of the initial seed radiation, with a particular emphasis on the possibility of having an LVS fundamental string network

Integer solutions to the anomaly equations for a class of chiral gauge theories

We find all the integer charge solutions to the equations for the cancellation of local gauge anomalies in a class of gauge theories which extend the Standard Model (SM) by a gauge group of the form $G \times U(1)$, where $G$ is an arbitrary semisimple compact Lie group. The SM fermions are assumed to be neutral under $G \times U(1)$ gauge interactions, while the new fermions transform in non-trivial representations of both the new and the SM gauge groups. Our analysis is valid also when the latter is embedded in an arbitrary semisimple compact Lie group. Theories with this structure have been recently studied as models of composite axions based on accidental symmetries and can provide a field theory resolution to the axion quality problem. We apply our results to cases of phenomenological interest and prove the existence of charge assignments with Peccei-Quinn symmetry protected up to dimension 18.Comment: 26 pages. v2: one reference added and typos fixe

Catch-me-if-you-can: the overshoot problem and the weak/inflation hierarchy

Abstract We study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). LVS cosmology features a long kination epoch as the volume modulus rolls down the exponential slope towards the final minimum, with an energy density that scales as m s 4 $${m}_s^4$$ . It is a known fact that such a roll admits attractor tracker solutions, and if these are located the overshoot problem is solved. We show that, provided a sufficiently large hierarchy exists between the inflationary scale and the weak scale, this will always occur in LVS as initial seed radiation grows into the tracker solution. The consistency requirement of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales — an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins, both universal and model-dependent, of the initial seed radiation (or matter). One particularly interesting case is that of a fundamental string network arising from brane inflation — this may lead to an early epoch in which the universe energy density principally consists of gravitational waves, while an LVS fundamental string network survives into the present universe

Exploring the holographic swampland

We extend studies of holographic aspects of moduli stabilisation scenarios to both fibred versions of LVS and the type IIA DGKT flux vacua. We study the holographic properties of the low-energy moduli Lagrangian that describes both the AdS vacuum and also small perturbations about it. For type IIA vacua in the large-volume regime, the CFT data (operator dimensions and higher-point interactions) take a universal form independent of the many arbitrary flux choices, as was previously found for LVS stabilisation. For these IIA vacua the conformal dimensions of the dual operators are also, surprisingly, all integers, although we do not understand a deeper reason why this is so. In contrast to behaviour previously found for LVS and KKLT, the fibred models also admit cases of mixed double-trace operators (for two different axion fields) where the anomalous dimension is positive

Integer conformal dimensions for type IIa flux vacua

We give a concise argument that supersymmetric anti–de Sitter type IIA DeWolfe-Giryavets-Kachru-Taylor flux vacua on general Calabi-Yau’s have, interpreted holographically, integer conformal dimensions for low-lying scalar primaries in the dual conformal field theory. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. For the Kähler moduli and dilaton, there is one operator with Δ=10 and h1,1− operators with Δ=6, whereas the corresponding axions have Δ=11 and Δ=5. For the complex structure moduli, the h2,1 saxions have Δ=2, and the axions Δ=3. We give a tentative discussion of the origin of these integers and effects that would modify these results

Kination, meet Kasner: on the asymptotic cosmology of string compactifications

Abstract We study runaway, kination-dominated epochs in string cosmology. We show how the apparent classical decompactification runaway of the volume modulus, described by a kination epoch in the 4-dimensional EFT, can be uplifted to a classical Kasner solution in 10d in which the non-compact dimensions collapse towards a Big Crunch. This can also be generalised for arbitrary spacetime and compactification dimensions. We conclude with some comments on how this picture is modified by quantum effects, and the need for both dynamical and kinematical Swampland constraints