14 problems

Let the moduli space of an effective theory be equipped with its field-space metric, and consider a point at infinite geodesic distance. Swampland Distance Conjecture. For a viable…

Let $H_0=(h_1,h_2,\ldots,h_{N_{\rm F}})$ be the moduli matrix for the wall world-volume theory, with each $h_A$ an $N_{\rm C}$-vector of chiral superfields. Define the invariants ……

Let $\mathcal{L}^{(l)(\mathrm{SD})}(\kappa)$ denote the loop-order $l$ weak-field effective Lagrangian in a constant self-dual background, with fine-structure constant $\alpha$, ma…

Fix a spacetime dimension $d$ and a finite energy cutoff $\Lambda>0$ in $d$-dimensional Planck units. For each EFT, let $(\cF_{\rm EFT},\cD_{\rm EFT})$ denote the format and degree…

Let an EFT be an effective field theory compatible with quantum gravity. Its tame complexity is a pair of integers $(\cF_{\rm EFT},\cD_{\rm EFT})$ measuring the format and degree o…

Let the effective action be invariant under an $O(d,d)$ symmetry, with the indices of the $O(d)_+$ factor ranging from $1$ to $d$. Jayaprakash et al.'s symmetry-extension conjectur…

Consider an effective theory compatible with quantum gravity, and let its coupling functions be functions on the relevant moduli or field space. Tameness conjecture. These function…

The discussion concerns models with a dominant $bb\textbackslash phi^4$ term in the inflaton potential, for which radiative corrections would typically generate a mass term. Subdom…

Universal effective Lagrangian conjecture. The effective Lagrangian for all covariantly constant gauge fields has a universal form.

Tameness conjecture. Effective theories valid below a fixed cutoff scale that can be consistently coupled to quantum gravity need to be tame.

Low-energy incompleteness conjecture. The EFT of gravity is incomplete at low energies, and one or more additional EFT degrees of freedom are needed to account for a vacuum energy…

A massive spin-two field is denoted by $w_{\mu\nu}$, with mass $m$. Let $M_w$ be the scale associated with the interactions of $w_{\mu\nu}$, and let $M_{\mathrm{Pl}}$ denote the Pl…

Dimension-independence conjecture for parity-invariant scalar S-matrices. The result of the integral $I^D_{\mathtt s}(x)$ is independent of $D$ for $D\geq 4$.

Let an effective theory of quantum gravity be described in a region of field space, and consider moving sufficiently far in that field space. A tower of states is a collection of s…