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.Comment: 17 pages; v2: added clarifying comments and a referenc

Comments on M24_{24} representations and CY3CY_3 geometries

We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $\Omega$ 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.Comment: 27 pages, v2: minor additions, published versio

Mathieu moonshine in four dimensional N=1\mathcal{N}=1 theories

We show that the recently discovered Mathieu moonshine plays a role for certain four dimensional theories with $\mathcal{N}=1$ supersymmetry. These theories are obtained from the $E_8 \times E_8$ heterotic string theory by compactifying on toroidal orbifolds. We find that a universal contribution to the holomorphic gauge kinetic function can be expanded in such a way that the expansion coefficients are the dimensions of representations of the Mathieu group M$_{24}$.Comment: 15 page

New N=1 dualities from orientifold transitions - Part II: String Theory

We present a string theoretical description, given in terms of branes and orientifolds wrapping vanishing cycles, of the dual pairs of gauge theories analyzed in 1210.7799. Based on the resulting construction we argue that the duality that we observe in field theory is inherited from S-duality of type IIB string theory. We analyze in detail the complex cone over the zeroth del Pezzo surface and discuss an infinite family of orbifolds of flat space. For the del Pezzo case we describe the system in terms of large volume objects, and show that in this language the duality can be understood from the strongly coupled behavior of the O7^+ plane, which we analyze using simple F-theory considerations. For all cases we also give a different argument based on the existence of appropriate torsional components of the 3-form flux lattice. Along the way we clarify some aspects of the description of orientifolds in the derived category of coherent sheaves, and in particular we discuss the important role played by exotic orientifolds - ordinary orientifolds composed with auto-equivalences of the category - when describing orientifolds of ordinary quiver gauge theories.Comment: 51 pages, 16 figures; v2: minor changes, added references, published versio

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 $\epsilon$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $\epsilon$ 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.Comment: 30 page

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 $\mu^{4-p}\phi^p$. 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.Comment: 36 pages; v2: fixed typos, added reference