A bstract M5 branes probing D-type singularities give rise to 6d (1, 0) SCFTs with SO SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits.

We derive an upper bound on the free energy of a Bose gas at density $ \varrho $ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when $ a^3 \varrho \ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$, the free energy difference per volume between interacting and ideal Bose gases, is equal to $ 4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}) $. Here, $\varrho_c (T)$ denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and $ [⋅]_{+}= max \{⋅ , 0\}$ denotes the positive part.

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green’s function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.

We compute the string production rate at the end of inflation, using the string spectrum obtained in [M. Li, W. Song, Y. Song, Quantizing strings in de Sitter space, JHEP 0704 (2007) 042, hep-th/0701258] in a near-de Sitter space. Our result shows that highly excited strings are hardly produced, thus the simple slow-roll inflation alone does not offer a cosmic string production mechanism.