MIT Center for Theoretical Physics – a Leinweber Institute

We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4D F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be $\sim 10^{85}$–$10^{90}$. We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.

Recent measurements of baryon acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI) have been interpreted to suggest that dark energy may be evolving. In this work, we examine how prior choices affect such conclusions. Specifically, we study the biases introduced by the customary use of uniform priors on the Chevallier-Polarski-Linder (CPL) parameters, $w_0$ and $w_a$, when assessing evidence for evolving dark energy. To do so, we construct theory-informed priors on $(w_0, w_a)$ using a normalizing flow (NF), trained on two representative quintessence models, which learns the distribution of these parameters conditional on the underlying $Λ$CDM parameters. In the combined $\textit{Planck}$ CMB + DESI BAO analysis we find that the apparent tension with a cosmological constant in the CPL framework can be reduced from $\sim 3.1σ$ to $\sim 1.3σ$ once theory-informed priors are applied, rendering the result effectively consistent with $Λ$CDM. For completeness, we also analyze combinations that include Type Ia supernova data, showing similar shifts toward the $Λ$CDM limit. Taken together, the observed sensitivity to prior choices in these analyses arises because uniform priors – often mischaracterized as “uninformative” – can actually bias inferences toward unphysical parameter regions. Consequently, our results underscore the importance of adopting physically motivated priors to ensure robust cosmological inferences, especially when evaluating new hypotheses with only marginal statistical support. Lastly, our NF-based framework achieves these results by post-processing existing MCMC chains, requiring $\approx 1$ hour of additional CPU compute time on top of the base analysis – a dramatic speedup over direct model sampling that highlights the scalability of this approach for testing diverse theoretical models.

We introduce a novel numerical method to obtain the gluon splitting rates in an anisotropic QCD plasma in the AMY formalism, suitable for an anisotropic collision kernel. The method extends previous works by decomposing the additional angular information into Fourier modes, resulting in a significantly larger system of differential equations to solve numerically. It is then tested by calculating the rates for a simple anisotropic model for the collision kernel, which is compared to a thermal system. Remarkably, the obtained rates can be well-approximated by the rates calculated from an angular-averaged collision kernel, while still deviating significantly from equilibrium. An isotropic model for the collision kernel that is commonly used in QCD kinetic theory simulations, and which relies on the infrared temperature $T_*$ and an effective Debye mass, leads to rates that significantly deviate from the nonequilibrium rate, particularly at smaller parton energies.

We show that recent measurements of substructure-dependent jet suppression constrain the value of the resolution length of the droplets of quark-gluon plasma (QGP) formed in heavy ion collisions. This resolution length, $L_{\rm res}$, is defined such that the medium can only resolve partons within a jet shower that are separated by more than $L_{\rm res}$. We first use Hybrid Model calculations to reproduce ALICE measurements of the scaled Soft Drop angle $θ_g$ for anti-$k_t$$R = 0.2$ jets reconstructed from charged-particle tracks. We find that the narrowing of the $θ_g$-distribution in PbPb collisions compared to pp collisions that is seen in the ALICE data rules out a picture of fully coherent energy loss ($L_{\rm res} = \infty$) where each entire parton shower loses energy to the plasma as if it were a single unresolved colored object. We then use Hybrid Model calculations to reproduce ATLAS measurements of $dR_{12}$, the Soft Drop angle obtained by applying the Soft Drop grooming procedure to all charged-particle tracks in $R=1$ jets reconstructed from $R = 0.2$ skinny subjets. Our analysis demonstrates that the ATLAS measurements of $R_{\rm AA}$ for such $R = 1$ jets as a function of $dR_{12}$ are inconsistent with a picture of fully incoherent energy loss ($L_{\rm res} = 0$) in which every splitting in a parton shower is immediately resolved by the plasma. We find that our Hybrid Model calculations agree best with the ATLAS measurements if QGP has a finite, nonzero, resolution length $L_{\rm res}\sim (1-2)/(πT)$. For the first time, jet substructure measurements are constraining the resolution length of QGP from below, as well as from above.