Snowmass Theory Frontier Report
This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process.
hep-ph↗
arXiv subjects
S. Kachru
Publications and source records attributed to S. Kachru.
Quantum critical metals in $d=3+1$
We study the problem of disorder-free metals near a continuous Ising nematic quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the `Yukawa' coupling between the electrons and undamped bosons (nematic order parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the `marginal Fermi liquid' phenomenology\cite{Varma}. We discuss a large N theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.
cond-mat.str-el↗
On the Taxonomy of Flux Vacua
We investigate several predictions about the properties of IIB flux vacua on Calabi-Yau orientifolds, by constructing and characterizing a very large set of vacua in a specific example, an orientifold of the Calabi-Yau hypersurface in $WP^{4}_{1,1,1,1,4}$. We find support for the prediction of Ashok and Douglas that the density of vacua on moduli space is governed by ${\rm det}(-R - ω)$ where $R$ and $ω$ are curvature and Kähler forms on the moduli space. The conifold point $ψ=1$ on moduli space therefore serves as an attractor, with a significant fraction of the flux vacua contained in a small neighborhood surrounding $ψ=1$. We also study the functional dependence of the number of flux vacua on the D3 charge in the fluxes, finding simple power law growth.
hep-th↗
Bouncing Brane Cosmologies from Warped String Compactifications
We study the cosmology induced on a brane probing a warped throat region in a Calabi-Yau compactification of type IIB string theory. For the case of a BPS D3-brane probing the Klebanov-Strassler warped deformed conifold, the cosmology described by a suitable brane observer is a bouncing, spatially flat Friedmann-Robertson-Walker universe with time-varying Newton's constant, which passes smoothly from a contracting to an expanding phase. In the Klebanov-Tseytlin approximation to the Klebanov-Strassler solution the cosmology would end with a big crunch singularity. In this sense, the warped deformed conifold provides a string theory resolution of a spacelike singularity in the brane cosmology. The four-dimensional effective action appropriate for a brane observer is a simple scalar-tensor theory of gravity. In this description of the physics, a bounce is possible because the relevant energy-momentum tensor can classically violate the null energy condition.
hep-th↗
Supersymmetry Changing Bubbles in String Theory
We give examples of string compactifications to 4d Minkowski space with different amounts of supersymmetry that can be connected by spherical domain walls. The tension of these domain walls is tunably lower than the 4d Planck scale. The ``stringy'' description of these walls is known in terms of certain configurations of wrapped Dirichlet and NS branes. This construction allows us to connect a variety of vacua with 4d N=4,3,2,1 supersymmetry.
hep-th↗
Small Numbers from Tunneling Between Brane Throats
Generic classes of string compactifications include ``brane throats'' emanating from the compact dimensions and separated by effective potential barriers raised by the background gravitational fields. The interaction of observers inside different throats occurs via tunnelling and is consequently weak. This provides a new mechanism for generating small numbers in Nature. We apply it to the hierarchy problem, where supersymmetry breaking near the unification scale causes TeV sparticle masses inside the standard model throat. We also design naturally long-lived cold dark matter which decays within a Hubble time to the approximate conformal matter of a long throat. This may soften structure formation at galactic scales and raises the possibility that much of the dark matter of the universe is conformal matter. Finally, the tunnelling rate shows that the coupling between throats, mediated by bulk modes, is stronger than a naive application of holography suggests.
hep-th↗
Generating Small Numbers by Tunneling in Multi-Throat Compactifications
A generic F-theory compactification containing many D3 branes develops multiple brane throats. The interaction of observers residing inside different throats involves tunneling suppression and, as a result, is very weak. This suggests a new mechanism for generating small numbers in Nature. One application is to the hierarchy problem: large supersymmetry breaking near the unification scale inside a shallow throat causes TeV-scale SUSY-breaking inside the standard-model throat. Another application, inspired by nuclear-decay, is in designing naturally long-lived particles: a cold dark matter particle residing near the standard model brane decays to an approximate CFT-state of a longer throat within a Hubble time. This suggests that most of the mass of the universe today could consist of CFT-matter and may soften structure formation at sub-galactic scales. The tunneling calculation demonstrates that the coupling between two throats is dominated by higher dimensional modes and consequently is much larger than a naive application of holography might suggest.
hep-th↗
Lectures on Warped Compactifications and Stringy Brane Constructions
In these lectures, two different aspects of brane world scenarios in 5d gravity or string theory are discussed. In the first two lectures, work on how warped compactifications of 5d gravity theories can change the guise of the hierarchy problem and the cosmological constant problem is reviewed, and a discussion of several issues which remain unclear in this context is provided. In the next two lectures, microscopic constructions in string theory which involve D-branes wrapped on cycles of Calabi-Yau manifolds are described. The focus is on computing the superpotential in the brane worldvolume field theory. Such calculations may be a necessary step towards understanding e.g. supersymmetry breaking and moduli stabilization in stringy realizations of such scenarios, and are of intrinsic interest as probes of the quantum geometry of the Calabi-Yau space.
hep-th↗
Tension is Dimension
We propose a simple universal formula for the tension of a D-brane in terms of a regularized dimension of the associated conformal field theory statespace.
hep-th↗
4d Conformal Field Theories and Strings on Orbifolds
We propose correspondences between 4d quantum field theories with N=2,1,0 (super)conformal invariance and Type IIB string theory on various orbifolds. We argue using the spacetime string theory, and check using the beta functions (exactly for N=2,1 and so far at 1-loop for the gauge couplings in the N=0 case), that these theories have conformal fixed lines. The latter case potentially gives well-defined non-supersymmetric vacua of string theory, with a mechanism for making the curvature and cosmological constant small at nontrivial string coupling. We suggest a correspondence between nonsupersymmetric conformal fixed lines and nonsupersymmetric string vacua with vanishing vacuum energy.
hep-th↗
On the Matrix Description of Calabi-Yau Compactifications
We point out that the matrix description of M-theory compactified on Calabi-Yau threefolds is in many respects simpler than the matrix description of a $T^6$ compactification. This is largely because of the differences between D6 branes wrapped on Calabi-Yau threefolds and D6 branes wrapped on six-tori. In particular, if we define the matrix theory following the prescription of Sen and Seiberg, we find that the remaining degrees of freedom are decoupled from gravity.
hep-th↗
Matrix Description of Interacting Theories in Six Dimensions
We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of $N$ instantons in $\IR^4$.
hep-th↗
Geometric Singularities and Enhanced Gauge Symmetries
Using ``Tate's algorithm,'' we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small $SO(32)$ instantons, and discover new mixed perturbative/non-perturbative gauge symmetry enhancements. Upon further toroidal compactification to 4 dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.
hep-th↗
SUSY Gauge Dynamics and Singularities of 4d N=1 String Vacua
Many N=1 heterotic string compactifications exhibit physically mysterious singularities at codimension one in the moduli space of vacua. At these singularities, Yukawa couplings of charged fields develop poles as a function of the moduli. We explain these conformal field theory singularities, in a class of examples, as arising from non-perturbative gauge dynamics of non-perturbative gauge bosons (whose gauge coupling is the sigma model coupling) in the string theory.
hep-th↗
N=1 Dual String Pairs and Gaugino Condensation
We study a class of four-dimensional N=1 heterotic string theories which have nontrivial quantum dynamics arising from asymptotically free gauge groups. These models are obtained by orbifolding 4d N=2 heterotic/type II dual pairs by symmetries which leave unbroken products of nonabelian gauge groups (without charged matter) in a ``hidden sector'' on the heterotic side. Such models are expected to break supersymmetry through gaugino condensation in the hidden sector. We find a dual description of the effects of gaugino condensation on the type II side, where the corresponding superpotential arises at tree level. We speculate that the conformal field theory underlying the type II description may be related to a class of geometrical nonsupersymmetric string compactifications.
hep-th↗
Nonperturbative Results on the Point Particle Limit of N=2 Heterotic String Compactifications
Using heterotic/type II string duality, we obtain exact nonperturbative results for the point particle limit (alpha' -> 0) of some particular four dimensional, N=2 supersymmetric compactifications of heterotic strings. This allows us to recover recent exact nonperturbative results on N=2 gauge theory directly from tree-level type II string theory, which provides a highly non-trivial, quantitative check on the proposed string duality. We also investigate to what extent the relevant singular limits of Calabi-Yau manifolds are related to the Riemann surfaces that underlie rigid N=2 gauge theory.
hep-th↗
(0,2) Landau-Ginzburg Theory
A large class of (0,2) Calabi-Yau $σ$-models and Landau-Ginzburg orbifolds are shown to arise as different ``phases'' of supersymmetric gauge theories. We find a phenomenon in the Landau-Ginzburg phase which may enable one to understand which Calabi-Yau $σ$-models evade destabilization by worldsheet instantons. Examples of (0,2) Landau-Ginzburg vacua are analyzed in detail, and several novel features of (0,2) models are discussed. In particular, we find that (0,2) models can have different quantum symmetries from the (2,2) models built on the same Calabi-Yau manifold, and that a new kind of topology change can occur in (0,2) models of string theory.
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