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We study BPS spectra of D-branes on local Calabi-Yau threefolds O(-p)circle plus O(p-2) -> P-1 with p = 0,1, corresponding to 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., Communications in Mathematical Physics, 388, ISSN:1432-0916, ISSN:0010-3616

We propose a formula for the exact central charge of a B-type D-brane that is expected to hold in all regions of the Kahler moduli space of a Calabi-Yau. For Landau-Ginzburg orbifolds we propose explicit expressions for the mathematical objects that enter into the central charge formula. We show that our results are consistent with results in FJRW theory and the hemisphere partition function of the gauged linear sigma model., 91 pages, 2 figures, typos corrected, references added. Published version

We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-many perturbative invariants of the closed oriented 3-manifold. The conjecture is that this expansion coincides with the perturbative expansion of the Witten-Reshetikhin-Turaev invariants at roots of unity $q=e^{2 \pi i/r}$ with $r$ odd, in the limit $r \to \infty$. We provide numerical evidence for our conjecture., Comment: 22 pages, 2 figures; v2: published version

In these notes, we provide an introduction to the hemisphere partition function of 2d $(2,2)$ supersymmetric gauge theories, and discuss its relation to the "D-brane central charge" which were studied in superstring theory, in 2d supersymmetric quantum field theory, and in topological string theory. We also discuss relation to "macroscopic loop" in matrix models. They are mostly reviews of the work by the authors, but contains some new results such as the partition function for a rotated supersymmetry as well as the differential equations.

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group $SL(N, \mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theory $T_{N}[M]$. We establish a dictionary for this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, in particular for non-maximal punctures and $N>2$. We also highlight the non-Abelian description of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its Higgsing prescription and the resulting `refinement' in complex CS theory. This paper is a companion to our shorter paper arXiv:1510.03884, which summarizes our main results., 129 pages (sorry), 22 figures

We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d $(2,0)$ theory, which is compactified on a 3-manifold $\hat{M}$. We identify such defects in various corners of the 3d-3d correspondence, namely in 3d $SL(N,\mathbb{C})$ Chern-Simons theory, in 3d $\mathcal{N}=2$ theory, in 5d $\mathcal{N}=2$ super Yang-Mills theory, and in the M-theory holographic dual. We can make quantitative checks of the 3d-3d correspondence by computing partition functions at each of these theories. This Letter is a companion to a longer paper, which contains more details and more results., 6 pages, 3 figures

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum K\"ahler moduli space of these varieties and find no disagreement with existing results in the literature., Comment: v3: 46 pages, 1 figure. Corrected phase structure of general linear determinantal varieties. Typos corrected

We develop semiclassical methods to analyze the spectrum of BPS monopole operators for superconformal field theories in three dimensions with N=2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical holomorphic quantization of the solution of classical BPS equations of motion on the cylinder. We apply this formalism to various theories. We also use these techniques to compare the chiral rings of theories that might be related to each other via Seiberg dualities in four dimensions. We find that the change of basis transformations that generate dualities in four dimensions (homological operations) generically do not work in three dimensions in the presence of Chern-Simons terms. Instead, new theories generally arise this way. When dualities are possible, the Chern-Simons couplings need to satisfy certain arithmetic congruences. We also determine the spectrum of R-charges of the chiral ring operators by assembling them on a Hilbert series and by minimizing the coefficient of the maximum pole relative to the trial R-charge. This is related to volume minimization in theories with dual supergravity setups., Comment: 49 pages, 8 figures, JHEP format. v2: References added. A new subsection with quantum corrections to monopole operators is included. These quantum corrections restore some of the Seiberg dualities that did not match with the classical computation alone. Minor fix on one figure

We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds to the q->1 limit of the Chern-Simons theory while the strong-coupling regime is related to the q->0 limit. In the latter case, there is a logarithmic relationship between the respective coupling constants. We also show how the Chern-Simons matrix model arises by considering two-dimensional Yang-Mills theory with the Villain action. This leads to a U(1)^N theory which is the Abelianization of 2d Yang-Mills theory with the heat-kernel lattice action. In addition, we show that the character expansion of the Villain lattice action gives the q deformation of the heat kernel as it appears in q-deformed 2d Yang-Mills theory. We also study the relationship between the unitary and Hermitian Chern-Simons matrix models and the rotation of the integration contour in the corresponding integrals., 17 pages, Minor corrections to match the published version

We discuss a marginal deformation of the SL(2,R) x SU(2) x U(1)^4 WZW model, which describes string theory on AdS_3 x S^3 x T^4, that corresponds to warping the S^3 factor. This deformation breaks part of the N=(4,4) supersymmetry of the undeformed dual CFT to N=(0,4) supersymmetry. In the spirit of work by Giveon, Kutasov, and Seiberg, we construct the asymptotic spacetime symmetry algebra from worldsheet operators and find a restoration of (4,4) supersymmetry at discrete values of the deformation parameter. We explain this result from various perspectives: the worldsheet, supergravity, and from the singular D1-D5 CFT. The supergravity analysis includes an asymptotic symmetry computation of the level of the affine SU(2) R-symmetry, which arises purely from B-field contributions., Comment: 16 pages; v2: references added

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian.

We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include G\"odel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis., Comment: 24 pages + appendices

It is observed that three-dimensional G\"odel black holes can be promoted to exact string theory backgrounds through an orbifold of an hyperbolic asymmetric marginal deformation of the SL(2,R) WZW model. Tachyons are found in the spectrum of long strings. Uplifting these solutions in type IIB supergravity, extremal black holes are shown to preserve one supersymmetry in accordance with the BTZ limit. We also make connections with some recently discussed warped black hole solutions of topologically massive gravity, showing that they actually correspond to quotients of spacelike squashed AdS_3., Comment: 15 pages

In all the odd dimensions which allow Majorana spinors, we consider a gravitational Lagrangian possessing local Poincare invariance and given by the dimensional continuation of the Euler density in one dimension less. We show that the local supersymmetric extension of this Lagrangian requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. By maximal, we mean that in the right hand side of the anticommutator of the Majorana super charge appear all the possible central charges. The resulting action defines a Chern-Simons gauge theory for the maximal extension of the super-Poincare algebra. In these dimensions, we address the same problem for the AdS invariant gravity and we derive its supersymmetric extension for the minimal super-AdS algebra. The connection between both models is realized at the algebraic level through an expansion of their corresponding Lie super algebras. Within a procedure consistent with the expansion of the algebras, the local supersymmetric extension of the Poincare invariant gravity Lagrangian is derived from the super AdS one., Comment: 9 pages. Minor changes (typos and references added). Accepted in JHEP

The Kaluza-Klein compactification process is applied in five dimensions to CS gravity, for the anti-de Sitter and Poincar\'e groups, using the first order formalism. In this context some solutions are found and analyzed. Also, the conserved charges associated to the solutions are computed., Comment: Minor corrections

We explicitly calculate the induced gravity theory at the boundary of an asymptotically Anti-de Sitter five dimensional Einstein gravity. We also display the action that encodes the dynamics of radial diffeomorphisms. It is found that the induced theory is a four dimensional conformal gravity plus a scalar field. This calculation confirms some previous results found by a different approach., Revtex 8 pages, To be published in Phys. Rev. D