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DOE OSTI2023

Consistent truncations and dualities

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

AdS scale separation and the distance conjecture

It has been argued that orientifold vacua with fluxes in type IIA string theory can achieve moduli stabilisation and arbitrary decoupling between the AdS and KK scales upon sending certain unconstrained RR-flux quanta to infinity. In this paper, we find a novel scalar field in the open-string sector that allows us to interpolate between such IIA vacua that differ in flux quanta and find that the limit of large fluxes is nicely consistent with the distance conjecture. This shows that the massive IIA vacua pass an important Swampland criterion and suggests that scale-separated AdS vacua might not be in the Swampland. Our analysis also naturally suggests a flux analogue of “Reid’s fantasy” where flux vacua that differ in quantised flux numbers can be connected through trajectories in open-string field space and not just via singular domain walls.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Towards natural and realistic E 7 GUTs in F-theory

We consider phenomenological aspects of a natural class of Standard Model-like supersymmetric F-theory vacua realized through flux breaking of rigid E 7 gauge factors. Three generations of Standard Model matter are realized in many of these vacua. We further find that many other Standard Model-like features are naturally compatible with these constructions. For example, dimension-4 and 5 terms associated with proton decay are ubiquitously suppressed. Many of these features are due to the group theoretical structure of E 7 and associated F-theory geometry. In particular, a set of approximate global symmetries descends from the E 7 group, leading to exponential suppression of undesired couplings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Understanding KKLT from a 10d perspective

Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

An F-theory realization of the chiral MSSM with Z 2 -parity

Using F-theory we construct 4D N=1 SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi-Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell-Weil group and SU( 3 ) × SU( 2 ) singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant Z 2 charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. As a result, these inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the Z 2 into a U( 1 ) and the resulting discrete anomalies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Towards an “$\mathrm{AdS}_1$/$\mathrm{CFT}_0$” correspondence from the $\mathrm{D}$(-1)/$\mathrm{D}$7 system?

We argue that a type IIB Euclidean supergravity solution of the form $\mathbb{R}$ x S 1 x $\mathbb{T}$ 8 with imaginary self-dual F 1 flux through $\mathbb{R}$ x S 1 belongs to the chain of AdS d x S d x $\mathbb{T}$ 10-2d vacua with (imaginary) self-dual Fd flux, where d ≤ 5. Such vacua come from the near-horizon of D(d - 2)/D(8 - d) branes and are supersymmetric for odd values of d. For d = 1 we speculate that the hallmark of conformal symmetry for the matrix model dual is a vanishing free energy. The matrix dual was recently constructed by [1] by adding matrix interactions coming from strings stretching between the D(-1) and D7 branes to the IKKT matrix model. We find that the corresponding supergravity solution indeed has vanishing on-shell action. Specific F 5 fluxes need to be switched on as a consequence of (a T-dual version of) the Hanany-Witten effect.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Neutralizing topological obstructions to bubbles of nothing

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g 2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Flowing to higher dimensions: a new strongly-coupled phase on M2 branes

We describe a one-parameter family of new holographic RG flows that start from AdS 4 × S 7 and go to AdS 5 ˆ×B6, where B6 is conformal to a Kahler manifold and AdS 5 ˆ is Poincaré AdS 5 with one spatial direction compactified and fibered over B6. The new solutions “flow up dimensions,” going from the (2 + 1)-dimensional conformal field theory on M2 branes in the UV to a (3 + 1)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincare sections of the AdS 5 ˆ are the (3 + 1)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional N=2 supersymmetric flow in N=8 gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. As a result, the eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginary octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Searching the landscape of flux vacua with genetic algorithms

In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric T 6 as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Heterotic backgrounds via generalised geometry: moment maps and moduli

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) x $\mathbb{R}$ + generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory

We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits no chiral matter representations. We focus specifically on applications to realizations of the Standard Model gauge group and chiral matter spectrum through breaking of rigid exceptional gauge groups E 7 , E 6 , which are ubiquitous in the 4D F-theory landscape. Supplemented by an intermediate SU(5) group, these large classes of models give natural constructions of Standard Model-like theories with small numbers of generations of matter in F-theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

New solutions with accelerated expansion in string theory

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w = –1 and another accumulating near w = –1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. Here, we briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Do we live in the swampland?

A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a theory of quantum gravity. The natural question is if the standard model of particle physics, possibly with some minimal extensions, are in the swampland — we are in trouble if the answer to this question is yes. We discuss this question in view of the recent swampland conjectures. We prove a no-go theorem concerning the modification of the Higgs sector. Moreover, we find that QCD axion is incompatible with the recent swampland conjectures, unless some sophisticated possibilities are considered. We discuss the implications of this result for spontaneous breaking of CP symmetry. We comment on dynamical supersymmetry breaking as well as the issue of multi-valuedness of the potential. We also propose a refinement of the de Sitter swampland conjecture.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

On the τ-Compactness of Products of τ -Measurable Operators Adjoint to Semi-Finite Von Neumann Algebras

Let M be the von Neumann algebra of operators in a Hilbert space H and τ be an exact normal semi-finite trace on M. We obtain inequalities for permutations of products of τ-measurable operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood, and Pólya) of products of τ -measurable operators and a sufficient condition of orthogonality of certain nonnegative τ-measurable operators. We state sufficient conditions of the τ –compactness of products of self-adjoint τ -measurable operators and obtain a criterion of the τ -compactness of the product of a nonnegative τ-measurable operator and an arbitrary τ -measurable operator. We present an example that shows that the nonnegativity of one of the factors is substantial. We also state a criterion of the elementary nature of the product of nonnegative operators from M . All results are new for the *-algebra B(H) of all bounded linear operators in H endowed with the canonical trace τ = tr.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Accidental inflation from Kähler uplifting

We analyze the possibility of realizing inflation with a subsequent dS vacuum in the Käahler uplifting scenario. The inclusion of several quantum corrections to the 4d effective action evades previous no-go theorems and allows for construction of simple and successful models of string inflation. The predictions of several benchmark models are in accord with current observations, i.e., a red spectral index, negligible non-gaussianity, and spectral distortions similar to the simplest models of inflation. A particularly interesting subclass of models are ''left-rolling'' ones, where the overall volume of the compactified dimensions shrinks during inflation. We call this phenomenon ''inflation by deflation'' (IBD), where deflation refers to the internal manifold. This subclass has the appealing features of being insensitive to initial conditions, avoiding the overshooting problem, and allowing for observable running α ∼ 0.012 and enhanced tensor-to-scalar ratio r ∼ 10{sup −5}. The latter results differ significantly from many string inflation models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Moduli inflation in five-dimensional supergravity models

We propose a simple but effective mechanism to realize an inflationary early universe consistent with the observed WMAP, Planck and/or BICEP2 data, which would be incorporated in various supersymmetric models of elementary particles constructed in the (effective) five-dimensional spacetime. In our scenario, the inflaton field is identified with one of the moduli appearing when the fifth direction is compactified, and a successful cosmological inflation without the so-called η problem can be achieved by a very simple moduli stabilization potential. We also discuss the related particle cosmology during and (just) after the inflation, such as the (no) cosmological moduli problem.

79 ASTRONOMY AND ASTROPHYSICS↗