We consider compactifications of type II string theory using exact internal CFT's with central charge $c=9+ε$, $|ε| \ll 1$, leading to an effective potential for the dilaton. For $ε>0$ the potential is positive and the dilaton is ultimately driven to weak coupling. For $ε<0$ the dilaton is driven to strong coupling, but we can stabilise the background by including D-branes. The resulting minimum admits an $AdS_4$ solution where the cosmological constant is of the order $ε^3$ and the string coupling constant is of order $ε$. Furthermore these CFT's typically do not possess any massless or tachyonic modes. Thus these vacua provide exact CFT descriptions of moduli stabilisation in weakly coupled string theory.
Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms $(B_2,C_2)$ in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D $\mathcal{N}=1$ $F$-term scalar potentials at higher orders in the $α^{\prime}$ and $g_{s}$ expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependen…
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 an…
Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau threefolds with hundreds of Kähler moduli is notoriously hard. This is due not just to the very fast increase of the computational complexity with the number of moduli, but also to the fact that the scalar potential depends in general on the supergravity variables only implicitly. In fact, the supergravity chiral coordinates are 4-cycle volume moduli but the Kähler potential is an explicit function of the 2-cycle moduli and inverting between these two variables is in general impossible. In this pape…
Standard results in 4d N=1 string compactifications assign a number of moduli to each space-time filling D-brane, computed by analysing the D-brane action in a fixed background. We revisit such conventional wisdom and argue that this naive counting of open string moduli is incorrect, in the sense that some of them will be lifted when making dynamical the bulk degrees of freedom. We explicitly discuss this effect for D6-branes wrapping special Lagrangian three-cycles, showing that some geometric and Wilson line moduli are lifted even before taking into account worldsheet instanton effects. From…
We propose a new mechanism of (geometric) moduli stabilisation in type IIB/F-theory four-dimensional compactifications on Calabi-Yau manifolds, in the presence of 7-branes, that does not rely on non-perturbative effects. Complex structure moduli and the axion-dilaton system are stabilised in the standard way, without breaking supersymmetry, using 3-form internal fluxes. Kähler class moduli stabilisation utilises perturbative string loop corrections, together with internal magnetic fields along the D7-branes world-volume leading to Fayet-Iliopoulos D-terms in the effective supergravity action. …
Intersecting D6-branes provide a geometrically intuitive road to stringy particle physics models, where D6-branes stuck at orbifold singularities can lead to the stabilisation of deformation moduli, and the QCD axion can arise from the open string sector in a very constrained way compared to pure field theory. We demonstrate this interplay of different physical features here through an explicit model.
We discuss deformations of orbifold singularities on tilted tori in the context of Type IIA orientifold model building with D6-branes on special Lagrangian cycles. Starting from $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, we mod out an additional $\mathbb{Z}_3$ symmetry to describe phenomenologically appealing backgrounds and reduce to $\mathbb{Z}_3$ and $Ω\mathcal{R}$ invariant orbits of deformations. While D6-branes carrying SO(2N) or USp(2N) gauge groups do not constrain deformations, D6-branes with U(N) gauge groups develop non-vanishing D-terms if they couple to previously singular, now def…
We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of $p$-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, for which we derive a no-go result for de Sitter extrema. We classify branches of supersymmetric and non-supe…
A parametrization of (super) moduli space near the corners corresponding to bosonic or Neveu-Schwarz open string degenerations is introduced for worldsheets of arbitrary topology. With this parametrization, Feynman graph polynomials arise as the $α' \to 0$ limit of objects on moduli space. Furthermore, the integration measures of string theory take on a very simple and elegant form.
Flux moduli stabilisation, Supergravity algebras and no-go theorems
我们对通量诱导的12 d代数进行了一个完全的分类，该分类与N=1的II型定向折叠模型的集合相容，这些模型是T-对偶不变的，并且被T^6/（Z_2 x Z_2）各向同性轨道折叠的对称性所允许。分类是在IIB型框架中进行的，其中只有H_3和Q通量。然后，我们研究不去定理，制定在IIA型框架，存在的Minkowski/德西特（Mkw/dS）真空。通过推导IIA型和IIB型中三个模（S，T和U）的势能源之间的字典，我们能够将代数结果和不可行定理结合起来。其结果是一个系统的程序，用于识别现象可行的模型，其中Mkw/dS真空可能存在。我们提出了一个完整的表格，允许代数和可行性，其产生的标量势，我们点在模型的立场，任何机会产生一个完全稳定的真空。
We study moduli stabilisation in four-dimensional $N=1$ supergravity theories which originate from compactifications of the heterotic string on certain manifolds with $SU(3)$ structure. These theories have a non-trivial superpotential generated from geometric flux and, in general, D-terms associated to anomalous $U(1)$ symmetries. We show that, at the perturbative level, there are no supersymmetry preserving vacua. However, subject to a certain technical condition on the D-terms which aligns the extrema of the F-term and D-term potentials, $\partial_iV_F=\partial_iV_D=0$, we find at the pertur…
The statistics of the supersymmetry breaking scale in the string landscape has been extensively studied in the past finding either a power-law behaviour induced by uniform distributions of F-terms or a logarithmic distribution motivated by dynamical supersymmetry breaking. These studies focused mainly on type IIB flux compactifications but did not systematically incorporate the Kähler moduli. In this paper we point out that the inclusion of the Kähler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacu…
We study the effective field theory of KKLT and LVS moduli stabilisation scenarios coupled to an anti-D3-brane at the tip of a warped throat. We describe the presence of the anti-brane in terms of a nilpotent goldstino superfield in a supersymmetric effective field theory. The introduction of this superfield produces a term that can lead to a de Sitter minimum. We fix the Kaehler moduli dependence of the nilpotent field couplings by matching this term with the anti-D3-brane uplifting contribution. The main result of this paper is the computation, within this EFT, of the soft supersymmetry brea…
String theory on $AdS_3 \times S^3 \times T^4$ has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string coupling, only four of the moduli affect the energies. In the RR background the only effect of these moduli is to change the radius of curvature of the background. On the other hand, in the NSNS background, the moduli introduce worldsheet interactions which enable the use of integrability methods to solve the spectral problem. Our results show that the worldshee…
String theory realisations of the QCD axion are often said to belong to the anthropic window where the decay constant is around the GUT scale and the initial misalignment angle has to be tuned close to zero. In this paper we revisit this statement by studying the statistics of axion physics in the string landscape. We take moduli stabilisation properly into account since the stabilisation of the saxions is crucial to determine the physical properties of the corresponding axionic partners. We focus on the model-independent case of closed string axions in type IIB flux compactifications and find…
We study string loop corrections to the gravity kinetic terms in type IIB compactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of $D7$-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the $D7$-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kähler modu…
Moduli Stabilisation for ADD and the Dark Dimension Scenario
Durham University（杜伦大学）；Università di Bologna（博洛尼亚大学）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）；Università di Trieste（的里雅斯特大学）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
In this work we investigate the moduli stabilisation problem and the requirements for de Sitter vacua within the framework of type IIB string theory. Using perturbative effects arising from the various sources such as $α^\prime$ corrections, logarithmic as well as KK and winding-type string-loop corrections along with the higher derivative $F^4$-contributions, we present a moduli stabilisation scheme in which the overall volume is realised at exponentially large values such that $\langle {\cal V} \rangle \simeq e^{a/g_s^2}$ in the weak coupling regime, where $a$ is a parameter given as $a = \f…
Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is …
The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $α'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative $α'$ corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its pot…
Light-cone string diagrams have been used to reproduce the orbifold Euler characteristic of moduli spaces of punctured Riemann surfaces at low genus and with few punctures. Nakamura studied the meromorphic differential introduced by Giddings and Wolpert to characterise light-cone diagrams and introduced a class of graphs related to this differential. These Nakamura graphs were used to parametrise the cells in a light-cone cell decomposition of moduli space. We develop links between Nakamura graphs and realisations of the worldsheet as branched covers. This leads to a development of the combina…
