arXiv subjects

Timm Wrase

Publications and source records attributed to Timm Wrase.

At least 55 records · Page 3Linked to original sources

arXiv2017

A New Class of de Sitter Vacua in Type IIB Large Volume Compactifications

We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the `Large Volume Scenario' anti-de Sitter vacua, and can analogously be realised at parametrically large volume and weak string coupling, using standard ${\cal N}=1$ supergravity. For these new vacua, a positive vacuum energy is achieved from the inclusion of a small amount of flux-induced supersymmetry breaking in the complex structure and axio-dilaton sector, and no additional `uplift' contribution (e.g.~from anti-branes) is required. We show that the approximate no-scale structure of the effective theory strongly influences the spectrum of the stabilised moduli: one complex structure modulus remains significantly lighter than the supersymmetry breaking scale, and metastability requires only modest amounts of tuning. After discussing these general results, we provide a recipe for constructing de Sitter vacua on a given compactification manifold, and give an explicit example of a de Sitter vacuum for the compactification on the Calabi-Yau orientifold realised in $\mathbb{CP}^4_{11169}$. Finally, we note that these solutions have intriguing implications for phenomenology, predicting no superpartners in the spectrum below $\sim$50 TeV, and no WIMP dark matter.

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arXiv2017

Maximal Supersymmetry and B-Mode Targets

Extending the work of Ferrara and one of the authors, we present dynamical cosmological models of $α$-attractors with plateau potentials for $3α=1,2,3,4,5,6,7$. These models are motivated by geometric properties of maximally supersymmetric theories: M-theory, superstring theory, and maximal $N = 8$ supergravity. After a consistent truncation of maximal to minimal supersymmetry in a seven-disk geometry, we perform a two-step procedure: 1) we introduce a superpotential, which stabilizes the moduli of the seven-disk geometry in a supersymmetric minimum, 2) we add a cosmological sector with a nilpotent stabilizer, which breaks supersymmetry spontaneously and leads to a desirable class of cosmological attractor models. These models with $n_s$ consistent with observational data, and with tensor-to-scalar ratio $r \approx 10^{-2}- 10^{-3}$, provide natural targets for future B-mode searches. We relate the issue of stability of inflationary trajectories in these models to tessellations of a hyperbolic geometry.

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arXiv2016

Sneutrino Inflation with $α$-attractors

Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. We show that one can improve the latest version of this scenario and its consistency with the Planck data by embedding it in the theory of cosmological $α$-attractors.

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arXiv2016

String Theory Origin of Constrained Multiplets

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector $A_μ$, three complex scalars $ϕ^i$ and four 4d fermions $λ^0$, $λ^i$. These transform, in addition to the more familiar N=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear N=1 multiplets: four chiral multiplets $S$, $Y^i$ that satisfy $S^2=SY^i=0$ and contain the worldvolume fermions $λ^0$ and $λ^i$; and four chiral multiplets $W_α$, $H^i$ that satisfy $S W_α=0$ and $S \bar D_{\dot α} \bar H^{\bar \imath}=0$ and contain the vector $A_μ$ and the scalars $ϕ^i$. We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet $Φ$ that satisfies $S(Φ-\bar Φ)=0$, which is particularly interesting for inflationary cosmology.

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arXiv2016

Constrained superfields from an anti-D3-brane in KKLT

The KKLT construction of dS vacua relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this anti-D3-brane is an excited state in a supersymmetric theory since it can decay to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry spontaneously and one should be able to package all the world-volume fields on the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3-brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy $S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming publication) that the vector field $A_μ$ and the three scalars $ϕ^i$ give rise to a field strength multiplet $W_α$ and three chiral multiplets $H^i$ that satisfy the constraints $S W_α= \bar{D}_{\dot α} (S \bar H^i)=0$. This is the first time that such constrained multiplets appear in string theory constructions.

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arXiv2016

Linear Versus Non-linear Supersymmetry, in General

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM's: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.

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arXiv2016

Coupling the Inflationary Sector to Matter

We describe the coupling of matter fields to an inflationary sector of supergravity, the inflaton $Φ$ and a stabilizer $S$, in models where the Kahler potential has a flat inflaton direction. Such models include, in particular, advanced versions of the hyperbolic $α$-attractor models with a flat inflaton direction Kahler potential, providing a good fit to the observational data. If the superpotential is at least quadratic in the matter fields $U^{i}$, with restricted couplings to the inflaton sector, we prove that under certain conditions: i) The presence of the matter fields does not affect a successful inflationary evolution. ii) There are no tachyons in the matter sector during and after inflation. iii) The matter masses squared are higher than $3H^2$ during inflation. The simplest class of theories satisfying all required conditions is provided by models with a flat direction Kahler potential, and with the inflaton $Φ$ and a stabilizer $S$ belonging to a hidden sector, so that matter fields have no direct coupling to the inflationary sector in the Kahler potential and in the superpotential.

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arXiv2015

The general de Sitter supergravity component action

In this paper we review the appearance and utility of a nilpotent chiral multiplet in the context of supergravity, string theory and cosmology. Coupling a nilpotent chiral superfield to supergravity, one obtains what is called pure dS supergravity, a supergravity theory without scalar degrees of freedom that naturally has de Sitter (dS) solutions, and in which supersymmetry is non-linearly realized. We extend previous results that couple this dS supergravity to chiral and vector multiplets and derive the most general supergravity action for a single nilpotent chiral multiplet coupled to supergravity and an arbitrary number of chiral and vector multiplets.

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arXiv2015

De Sitter Supergravity Model Building

We present the explicit de Sitter supergravity action describing the interaction of supergravity with an arbitrary number of chiral and vector multiplets as well as one nilpotent chiral multiplet. The action has a non-Gaussian dependence on the auxiliary field of the nilpotent multiplet, however, it can be integrated out for an arbitrary matter-coupled supergravity. The general supergravity action with a given Kahler potential $K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent chiral multiplet consists of the standard supergravity action defined by $K$, $W$ and $f_{AB}$ where the scalar in the nilpotent multiplet has to be replaced by a bilinear combination of the fermion in the nilpotent multiplet divided by the Gaussian value of the auxiliary field. All additional contributions to the action start with terms quartic and higher order in the fermion of the nilpotent multiplet. These are given by a simple universal closed form expression.

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arXiv2015

Mock Modular Mathieu Moonshine Modules

We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory, any subgroup of Co_0 that fixes a 3-dimensional subspace of its unique non-trivial 24-dimensional representation commutes with a certain N=4 superconformal algebra. Similarly, any subgroup of Co_0 that fixes a 2-dimensional subspace of the 24-dimensional representation commutes with a certain N=2 superconformal algebra. Through the decomposition of the corresponding twined partition functions into characters of the N=4 (resp. N=2) superconformal algebra, we arrive at mock modular forms which coincide with the graded characters of an infinite-dimensional Z-graded module for the corresponding group. The Mathieu groups are singled out amongst various other possibilities by the moonshine property: requiring the corresponding weak Jacobi forms to have certain asymptotic behaviour near cusps. Our constructions constitute the first examples of explicitly realized modules underlying moonshine phenomena relating mock modular forms to sporadic simple groups. Modules for other groups, including the sporadic groups of McLaughlin and Higman--Sims, are also discussed.

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arXiv2015

$\overline{\rm D3}$ and dS

The role of the $\overline{\rm D3}$ brane in providing de Sitter vacua with spontaneously broken supersymmetry in the KKLT construction is clarified. The first step in this direction was explained in arXiv:hep-th/0301240, arXiv:hep-th/0308055: it was shown there that in the GKP background the bosonic contributions to the vacuum energy from the DBI and WZ term cancel for a D3 brane, but double for a $\overline{\rm D3}$ brane, leading to de Sitter vacua. The next step was taken in arXiv:1411.1121 where the analogous mechanism of the doubling (cancelation) of the $\overline{\rm D3}$ (D3) DBI and WZ terms was discovered in the presence of Volkov-Akulov fermions living on the brane, in a flat supergravity background. Here we confirm this mechanism of doubling/cancelation for the $\overline{\rm D3}$/D3 brane in the GKP supergravity background preserving $\mathcal{N}=1$, $d=4$ supersymmetry. We find that imaginary self-dual $G_{(3)}$ flux of type $(2,1)$ nicely removes the $SU(3)$ fermion triplet by giving it a large mass, while leaving the Volkov-Akulov goldstino, which is the $SU(3)$ singlet, massless. This makes the de Sitter landscape in D-brane physics clearly related to de Sitter vacua in effective $d=4$ supergravity with a nilpotent multiplet and spontaneously broken supersymmetry.

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arXiv2014

Comments on M$_{24}$ representations and $CY_3$ geometries

We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $Ω$ for certain $CY_3$ manifolds. We also discuss how the period vectors appear in flux compactifications on these $CY_3$ manifolds and work out the connection between the sporadic group M$_{24}$ and the Yukawa couplings in four dimensional theories that arise from heterotic string theory compactifications on these $CY_3$ manifolds.

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arXiv2014

Charting an Inflationary Landscape with Random Matrix Theory

We construct a class of random potentials for N >> 1 scalar fields using non-equilibrium random matrix theory, and then characterize multifield inflation in this setting. By stipulating that the Hessian matrices in adjacent coordinate patches are related by Dyson Brownian motion, we define the potential in the vicinity of a trajectory. This method remains computationally efficient at large N, permitting us to study much larger systems than has been possible with other constructions. We illustrate the utility of our approach with a numerical study of inflation in systems with up to 100 coupled scalar fields. A significant finding is that eigenvalue repulsion sharply reduces the duration of inflation near a critical point of the potential: even if the curvature of the potential is fine-tuned to be small at the critical point, small cross-couplings in the Hessian cause the curvature to grow in the neighborhood of the critical point.

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arXiv2014

Decoupling and de Sitter Vacua in Approximate No-Scale Supergravities

We study ${\cal N}=1$ supergravity with $N>1$ chiral superfields in which one of the fields has a Kähler potential of exact no-scale type. Such systems admit de Sitter (dS) solutions in which supersymmetry is predominantly broken by the no-scale field, with only a small contribution to the breaking coming from the other fields. Metastable dS vacua of this type were recently shown to be achievable by the finetuning of an $N\times N$ sub-matrix of the Hessian matrix at the critical point. We show that perturbatively small deformations of the no-scale Minkowski vacuum into dS are only possible when the spectrum of the no-scale vacuum, besides the no-scale field, contain an additional massless mode. The no-scale structure allows for a decoupling of $N-2$ fields, and metastability can be achieved by the tuning of ${\cal O}(N^0)$ parameters. We illustrate this scenario in several examples, and derive a geometric condition for its realisation in type IIB string theory. Supergravities in which the complex structure moduli space is a symmetric space, such as the string theory inspired STU-models, are non-generic and realise a modified version of the scenario. For the STU-model with a single non-perturbative correction we present an explicit analytic family of dS solutions that includes examples with quantised fluxes satisfying the O3-plane tadpole condition.

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arXiv2014

Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua

The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the world-volume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of $\mathbb{R}^{9,1}$ we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the anti-D3-brane we show that the DBI action and the WZ action combine and lead to the emergence of the goldstino multiplet which is responsible for spontaneous breaking of supersymmetry. This provides a string theoretic explanation for the supersymmetric uplifting term in the KKLT effective supergravity model supplemented by a nilpotent chiral multiplet.

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arXiv2014

The Powers of Monodromy

Flux couplings to string theory axions yield super-Planckian field ranges along which the axion potential energy grows. At the same time, other aspects of the physics remain essentially unchanged along these large displacements, respecting a discrete shift symmetry with a sub-Planckian period. After a general overview of this monodromy effect and its application to large-field inflation, we present new classes of specific models of monodromy inflation, with monomial potentials $μ^{4-p}ϕ^p$. A key simplification in these models is that the inflaton potential energy plays a leading role in moduli stabilization during inflation. The resulting inflaton-dependent shifts in the moduli fields lead to an effective flattening of the inflaton potential, i.e. a reduction of the exponent from a fiducial value $p_0$ to $p<p_0$. We focus on examples arising in compactifications of type IIB string theory on products of tori or Riemann surfaces, where the inflaton descends from the NS-NS two-form potential $B_2$, with monodromy induced by a coupling to the R-R field strength $F_1$. In this setting we exhibit models with $p=2/3,4/3,2,$ and $3$, corresponding to predictions for the tensor-to-scalar ratio of $r\approx 0.04, 0.09, 0.13,$ and $0.2$, respectively. Using mirror symmetry, we also motivate a second class of examples with the role of the axions played by the real parts of complex structure moduli, with fluxes inducing monodromy.

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arXiv2014

Analytic Classes of Metastable de Sitter Vacua

In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $ε$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $ε$ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale.

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arXiv2014

On Holographic Defect Entropy

We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions.

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