arXiv subjects

Ben Heidenreich

Publications and source records attributed to Ben Heidenreich.

At least 37 records · Page 2Linked to original sources

arXiv2020

Black Holes, Moduli, and Long-Range Forces

It is well known that an identical pair of extremal Reissner-Nordstrom black holes placed a large distance apart will exert no force on each other. In this paper, I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordstrom black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area. Analogous results hold for black branes.

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arXiv2020

Repulsive Forces and the Weak Gravity Conjecture

The Weak Gravity Conjecture is a nontrivial conjecture about quantum gravity that makes sharp, falsifiable predictions which can be checked in a broad range of string theory examples. However, in the presence of massless scalar fields (moduli), there are (at least) two inequivalent forms of the conjecture, one based on charge-to-mass ratios and the other based on long-range forces. We discuss the precise formulations of these two conjectures and the evidence for them, as well as the implications for black holes and for "strong forms" of the conjectures. Based on the available evidence, it seems likely that both conjectures are true, suggesting that there is a stronger criterion which encompasses both. We discuss one possibility.

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arXiv2020

Infinite Distance and Zero Gauge Coupling in 5d Supergravity

In this note, we prove that for all five-dimensional supergravities arising from M-theory compactified on a Calabi-Yau threefold, points of vanishing gauge coupling lie at infinite distance in the moduli space. Conversely, any point at infinite distance in the vector multiplet moduli space is a point of vanishing gauge coupling. This agrees with expectations from the Tower/Sublattice Weak Gravity Conjecture, the Swampland Distance Conjecture, and the Emergence Proposal.

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arXiv2019

Instanton Resummation and the Weak Gravity Conjecture

We develop methods for resummation of instanton lattice series. Using these tools, we investigate the consequences of the Weak Gravity Conjecture for large-field axion inflation. We find that the Sublattice Weak Gravity Conjecture implies a constraint on the volume of the axion fundamental domain. However, we also identify conditions under which alignment and clockwork constructions, and a new variant of N-flation that we devise, can evade this constraint. We conclude that some classes of low-energy effective theories of large-field axion inflation are consistent with the strongest proposed form of the Weak Gravity Conjecture, while others are not.

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arXiv2019

IIB flux non-commutativity and the global structure of field theories

We discuss the origin of the choice of global structure for six dimensional $(2,0)$ theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of $\mathcal{N}=4$ theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of $\mathcal{N}=4$ ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional $(1,0)$ theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects.

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arXiv2018

The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.

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arXiv2018

Emergence and the Swampland Conjectures

The Ooguri-Vafa Swampland Conjectures claim that in any consistent theory of quantum gravity, when venturing to large distances in scalar field space, a tower of particles will become light at a rate that is exponential in the field space distance. We provide a novel viewpoint on this claim: if we assume that a tower of states becomes light near a particular point in field space, and we further demand that loop corrections drive both gravity and the scalar to strong coupling at a common energy scale, then the requirement that the particles become light exponentially fast in the field-space distance in Planck units follows automatically. Furthermore, the same assumption of a common strong-coupling scale for scalar fields and gravitons implies that when a scalar field evolves over a super-Planckian distance, the average particle mass changes by an amount of order the cutoff energy. This supports earlier suggestions that significantly super-Planckian excursions in field space cannot be described within a single effective field theory. We comment on the relationship of our results to the Weak Gravity Conjecture.

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arXiv2017

Evidence for a Lattice Weak Gravity Conjecture

The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$.

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arXiv2016

S-duality in $\mathcal{N} = 1$ orientifold SCFTs

We present a general solution to the problem of determining all S-dual descriptions for a specific (but very rich) class of $\mathcal{N} = 1$ SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S-dual phases are described by quiver gauge theories coupled to specific types of conformal matter which we describe explicitly. We illustrate our construction with many examples, including S-dualities in previously unknown SCFTs.

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arXiv2016

Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarthmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.

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arXiv2016

Sharpening the Weak Gravity Conjecture with Dimensional Reduction

We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a "Lattice Weak Gravity Conjecture" that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.

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arXiv2016

Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity Conjecture

Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world and for pure mathematics. We sketch some implications of these ideas for models of inflation, for the QCD axion (and LIGO), for conformal field theory, and for algebraic geometry.

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arXiv2016

Negative Branes, Supergroups and the Signature of Spacetime

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3 branes, we show that $SU(0|N)$ supergroup theories are holographically dual to an exotic variant of type IIB string theory on $dS_{3,2} \times \bar S^5$, for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $\mathcal N=2 ~SU(N|M)$ gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

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arXiv2016

Experimental Considerations Motivated by the Diphoton Excess at the LHC

We consider the immediate or near-term experimental opportunities offered by some scenarios that could explain the new diphoton excess at the LHC. If the excess is due to a new particle $X_s$ at 750 GeV, additional new particles are required, providing further signals. If connected with naturalness, the $X_s$ may be produced in top partner decays. Then a $t'\bar t'$ signal, with $t'\to t X_s$ and $X_s\to gg$ dominantly, might be discovered by reinterpreting 13 TeV SUSY searches in multijet events with low MET and/or a lepton. If $X_s$ is a bound state of quirks, the signal events may be accompanied by an unusual number of soft tracks or soft jets. Other resonances including dilepton and photon+jet as well as dijet may lie at or above this mass, and signatures of hidden glueballs might also be observable. If the "photons" in the excess are actually long-lived particles decaying to photon pairs or to electron pairs, there are opportunities for detecting overlapping photons and/or unusual patterns of apparent photon-conversions in either $X_s$ or 125 GeV Higgs decays. There is also the possibility of events with a hard "photon" recoiling against a narrow isolated HCAL-only "jet", which, after the jet's energy is corrected for its electromagnetic origin, would show a peak at 750 GeV.

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arXiv2015

Weak Gravity Strongly Constrains Large-Field Axion Inflation

Models of large-field inflation based on axion-like fields with shift symmetries can be simple and natural, and make a promising prediction of detectable primordial gravitational waves. The Weak Gravity Conjecture is known to constrain the simplest case in which a single compact axion descends from a gauge field in an extra dimension. We argue that the Weak Gravity Conjecture also constrains a variety of theories of multiple compact axions including N-flation and some alignment models. We show that other alignment models entail surprising consequences for how the mass spectrum of the theory varies across the axion moduli space, and hence can be excluded if further conjectures hold. In every case that we consider, plausible assumptions lead to field ranges that cannot be parametrically larger than the Planck scale. Our results are strongly suggestive of a general inconsistency in models of large-field inflation based on compact axions, and possibly of a more general principle forbidding super-Planckian field ranges.

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arXiv2015

Strongly coupled phases of $\mathcal{N}=1$ S-duality

We analyze S-duality of orientifolds of the Calabi-Yau cone over the first del Pezzo surface ($dP_1$). The S-duals of known phases, described by quiver gauge theories, contain intrinsically strongly-coupled sectors. These sectors are realized by a higher multiplicity intersection of NS5 branes and D5 branes atop an O5 plane, and can be thought of as stuck at the infinite coupling point between two Seiberg-dual gauge theories. We argue that such sectors appear generically in orientifolds of non-orbifold singularities, where in many examples every orientifold phase contains such a sector. Understanding such sectors is therefore key to understanding orientifolds of Calabi-Yau singularities. We construct the strongly-coupled sectors for $dP_1$ orientifolds using deconfinement, and show that they have interesting, non-trivial properties. Using this construction, we verify the predictions of S-duality for $dP_1$.

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arXiv2015

Natural Supersymmetry in Warped Space

We explore the possibility of solving the hierarchy problem by combining the paradigms of supersymmetry and compositeness. Both paradigms are under pressure from the results of the Large Hadron Collider (LHC), and combining them allows both a higher confinement scale -- due to effective supersymmetry in the low energy theory -- and heavier superpartners -- due to the composite nature of the Higgs boson -- without sacrificing naturalness. The supersymmetric Randall-Sundrum model provides a concrete example where calculations are possible, and we pursue a realistic model in this context. With a few assumptions, we are led to a model with bulk fermions, a left-right gauge symmetry in the bulk, and supersymmetry breaking on the UV brane. The first two generations of squarks are decoupled, reducing LHC signatures but also leading to quadratic divergences at two loops. The model predicts light $W'$ and $Z'$ gauge bosons, and present LHC constraints on exotic gauge bosons imply a high confinement scale and mild tuning from the quadratic divergences, but the model is otherwise viable. We also point out that R-parity violation can arise naturally in this context.

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arXiv2013

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.

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