Babak Haghighat

Bio: Babak Haghighat is an academic researcher from Tsinghua University. The author has contributed to research in topics: String (physics) & Quiver. The author has an hindex of 20, co-authored 53 publications receiving 1588 citations. Previous affiliations of Babak Haghighat include Utrecht University & University of Bonn.

M-Strings

Abstract: M2 branes suspended between adjacent parallel M5 branes lead to light strings, the `M-strings' In this paper we compute the elliptic genus of M-strings, twisted by maximally allowed symmetries that preserve 2d (2,0) supersymmetry In a codimension one subspace of parameters this reduces to the elliptic genus of the (4,4) supersymmetric A_{n-1} quiver theory in 2d We contrast the elliptic genus of N M-strings with the (4,4) sigma model on the N-fold symmetric product of R^4 For N=1 they are the same, but for N>1 they are close, but not identical Instead the elliptic genus of (4,4) N M-strings is the same as the elliptic genus of (4,0) sigma models on the N-fold symmetric product of R^4, but where the right-moving fermions couple to a modification of the tangent bundle This construction arises from a dual A_{n-1} quiver 6d gauge theory with U(1) gauge groups Moreover we compute the elliptic genus of domain walls which separate different numbers of M2 branes on the two sides of the wall

Orbifolds of M-strings

Abstract: We consider M-theory in the presence of M parallel M5-branes prob- ing a transverse AN−1 singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition func- tion of this theory on a two-torus, with arbitrary supersymmetry preserving twists, using the topological vertex formalism. Alternatively, we show that this can also be obtained by computing the elliptic genus of an orbifold of recently studied M-strings. The resulting 2d theory is a (4,0) supersymmetric quiver gauge theory whose Higgs branch corresponds to strings propagating on the moduli space of SU(N) M−1 instan- tons on R 4 where the right-moving fermions are coupled to a particular bundle.

Strings of Minimal 6d SCFTs

Abstract: We study strings associated with minimal 6d SCFTs, which by defini- tion have only one string charge and no Higgs branch. These theories are labelled by a number n with 1 ≤ n ≤ 8 or n = 12. Quiver theories have previously been proposed which describe strings of SCFTs for n = 1,2. For n > 2 the strings interact with the bulk gauge symmetry. In this paper we find a quiver description for the n = 4 string using Sen's limit of F-theory and calculate its elliptic genus with localization techniques. This result is checked using the duality of F-theory with M-theory and topological string theory whose refined BPS partition function captures the elliptic genus of the SCFT strings. We use the topological string theory to gain insight into the elliptic genus for other values of n.

Integrability of the holomorphic anomaly equations

Abstract: We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in terms of almost holomorphic modular forms. The formalism provides in particular holomorphic expansions everywhere in moduli space including large radius points, the conifold loci, Seiberg-Witten points and the orbifold points. It can be also viewed as a very efficient method to solve higher genus closed string amplitudes in the 1/N2 expansion of matrix models with more then one cut.

F-Theory, Spinning Black Holes and Multi-string Branches

Abstract: We study 5d supersymmetric black holes which descend from strings of generic $$ \mathcal{N}=\left(1,\kern0.5em 0\right) $$ supergravity in 6d. These strings have an F-theory realization in 6d as D3 branes wrapping smooth genus g curves in the base of elliptic 3-folds. They enjoy (0, 4) worldsheet supersymmetry with an extra SU(2) L current algebra at level g realized on the left-movers. When the smooth curves degenerate they lead to multi-string branches and we find that the microscopic worldsheet theory flows in the IR to disconnected 2d CFTs having different central charges. The single string sector is the one with maximal central charge, which when wrapped on a circle, leads to a 5d spinning BPS black hole whose horizon volume agrees with the leading entropy prediction from the Cardy formula. However, we find new phenomena where this branch meets other branches of the CFT. These include multi-string configurations which have no bound states in 6 dimensions but are bound through KK momenta when wrapping a circle, as well as loci where the curves degenerate to spheres. These loci lead to black hole configurations which can have total angular momentum relative to a Taub-Nut center satisfying J 2 > M 3 and whose number of states, though exponentially large, grows much slower than those of the large spinning black hole.

From weak to strong coupling in ABJM theory

Abstract: The partition function of $${\mathcal{N}=6}$$ supersymmetric Chern–Simons-matter theory (known as ABJM theory) on $${\mathbb{S}^3}$$ , as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on $${{\rm AdS}_4\times\mathbb{C}\mathbb{P}^3}$$ and gives the correct N 3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in $${\mathbb{C}\mathbb{P}^3}$$ . We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.

Quantum Black Holes, Wall Crossing, and Mock Modular Forms

Abstract: We show that the meromorphic Jacobi form that counts the quarter-BPS states in N=4 string theories can be canonically decomposed as a sum of a mock Jacobi form and an Appell-Lerch sum. The quantum degeneracies of single-centered black holes are Fourier coefficients of this mock Jacobi form, while the Appell-Lerch sum captures the degeneracies of multi-centered black holes which decay upon wall-crossing. The completion of the mock Jacobi form restores the modular symmetries expected from $AdS_3/CFT_2$ holography but has a holomorphic anomaly reflecting the non-compactness of the microscopic CFT. For every positive integral value m of the magnetic charge invariant of the black hole, our analysis leads to a special mock Jacobi form of weight two and index m, which we characterize uniquely up to a Jacobi cusp form. This family of special forms and another closely related family of weight-one forms contain almost all the known mock modular forms including the mock theta functions of Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the mock modular forms appearing in the Mathieu and Umbral moonshine, as well as an infinite number of new examples.

Exact results in ABJM theory from topological strings

Abstract: Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and Trancanelli.

Atomic classification of 6D SCFTs

Abstract: Author(s): Heckman, JJ; Morrison, DR; Rudelius, T; Vafa, C | Abstract: We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven-branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules," using an analogy from chemistry. The second step has an interpretation via quiver-type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE-type nodes joined by conformal matter. A collection of highly non-trivial examples involving E8 small instantons probing an ADE singularity is shown to have an F-theory realization. This yields a classification of homomorphisms from ADE subgroups of SU(2) into E8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.