Exact WKB methods in SU(2) Nf = 1

We study in detail the Schrödinger equation corresponding to the four dimensional SU(2) $$ \mathcal{N} $$ N = 2 SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schrödinger operator using the TS/ST correspondence and Zamolodchikov’s TBA, again finding good agreement. In addition, we explore two aspects of the relationship between singularities of the Borel transformed WKB series and BPS states: BPS states of the 4d theory are related to singularities in the Borel transformed WKB series for the quantum periods, and BPS states of a coupled 2d+4d system are related to singularities in the Borel transformed WKB series for local solutions of the Schrödinger equation.

Fractionally charged BPS particles in M-string on 3D orbifolds

In this paper, we study the M-string realization of chiral [Formula: see text]-super-conformal field theory in 6 dimensions and its orbifold compactification down to three-dimensional (3D). We analyze its fractionally charged BPS particle spectrum in connection with effective 3D Chern–Simons gauge theory and the supersymmetric fractional quantum Hall effect in [Formula: see text] dimensions. We construct the set of underlying fractionally charged BPS particles in the ground state of the compactified M string and find that it contains 144 BPS states that are generated by four basic quasi-particles (two bosonic-like and two fermionic like) and their CPT conjugate. Two representations of the gauge bosons and the gauginos as condensates of the basic quasiparticles are found and explicit realizations are also given. Other features concerning generalizations are also discussed.

Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I

We study BPS spectra of D-branes on local Calabi-Yau threefolds $$\mathcal {O}(-p)\oplus \mathcal {O}(p-2)\rightarrow \mathbb {P}^1$$ O ( - p ) ⊕ O ( p - 2 ) → P 1 with $$p=0,1$$ p = 0 , 1 , corresponding to $$\mathbb {C}^3/\mathbb {Z}_{2}$$ C 3 / Z 2 and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.

Lifting 1/4-BPS states in AdS3× S3 × T4

We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold SymN(T4) to all orders in N. This allows us to compute how 1/4-BPS states of the D1-D5 system on AdS3 × S3 × T4 are lifted as we move away from the orbifold point. As an application we confirm a previous observation that in the large N limit not all 1/4-BPS states that can be lifted do get lifted. This provides evidence that the supersymmetric index actually undercounts the number of 1/4-BPS states at a generic point in the moduli space.

Stability of BPS states and weak coupling limits

We study the stability and spectrum of BPS states in $$ \mathcal{N} $$ N = 2 supergravity. We find evidence, and prove for a large class of cases, that BPS stability exhibits a certain filtration which is partially independent of the value of the gauge couplings. Specifically, for any perturbative value of any gauge coupling g ≪ 1, a BPS state can only decay to some constituents if those constituents do not become infinitely heavier than it in the vanishing coupling limit g → 0. This stability filtration can be mathematically formulated in terms of the monodromy weight filtration of the limiting mixed Hodge structure associated to the vanishing coupling limit. We study various implications of the result for the Swampland program which aims to understand such weak-coupling limits, specifically regarding the nature and presence of an infinite tower of light charged BPS states.

EFT and the SUSY index on the 2nd sheet

The counting of BPS states in four-dimensional \mathcal{N}=1𝒩=1 theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS_55. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders \beta^{-2},\beta^{-1},\beta^0β−2,β−1,β0. We also make a conjecture for O(\beta)O(β), where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.

Medium, Small and Medium Enterprises and Digital Platforms

Central Bureau of Statistics of the Republic of Indonesia (Indonesian: Badan Pusat Statistik / BPS) states the Indonesian economy experienced deflation of 0.1% in July 2020. The food, beverage, and tobacco group experienced deflation of 0.79% and contributed to deflation of 0.19%. Foodstuffs that contributed to deflation included shallots, broiled chicken, rice, garlic, cayenne pepper and sugar. This deflation in food and beverages indicates a decline in demand for food.

The Resurgent Structure of Quantum Knot Invariants

The asymptotic expansion of quantum knot invariants in complex Chern–Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of q-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear q-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte–Gaiotto–Gukov 3D-index, and thus is given by a counting of BPS states. We illustrate our conjectures explicitly by matching theoretically and numerically computed integers for the cases of the $$4_1$$ 4 1 and the $$5_2$$ 5 2 knots.

Weak gravity bounds in asymptotic string compactifications

We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

Quarter-BPS states, multi-symmetric functions and set partitions

We give a construction of general holomorphic quarter BPS operators in $$ \mathcal{N} $$ N = 4 SYM at weak coupling with U(N) gauge group at finite N. The construction employs the Möbius inversion formula for set partitions, applied to multi-symmetric functions, alongside computations in the group algebras of symmetric groups. We present a computational algorithm which produces an orthogonal basis for the physical inner product on the space of holomorphic operators. The basis is labelled by a U(2) Young diagram, a U(N) Young diagram and an additional plethystic multiplicity label. We describe precision counting results of quarter BPS states which are expected to be reproducible from dual computations with giant gravitons in the bulk, including a symmetry relating sphere and AdS giants within the quarter BPS sector. In the case n ≤ N (n being the dimension of the composite operator) the construction is analytic, using multi-symmetric functions and U(2) Clebsch-Gordan coefficients. Counting and correlators of the BPS operators can be encoded in a two-dimensional topological field theory based on permutation algebras and equipped with appropriate defects.