We study BPS spectra of D-branes on local Calabi-Yau threefolds
O
(
-
p
)
⊕
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.
The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL（N, C） and M being a knot ...complement： M = S3 ／K. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G = SL（N, C）. He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.
Many
N
=
(
2
,
2
)
two-dimensional nonlinear sigma models with Calabi–Yau target spaces admit ultraviolet descriptions as
N
=
(
2
,
2
)
gauge theories (gauged linear sigma models). We conjecture that ...the two-sphere partition function of such ultraviolet gauge theories—recently computed via localization by Benini et al. and Doroud et al.—yields the exact Kähler potential on the quantum Kähler moduli space for Calabi–Yau threefold target spaces. In particular, this allows one to compute the genus zero Gromov–Witten invariants for any such Calabi–Yau threefold without the use of mirror symmetry. More generally, when the infrared superconformal fixed point is used to compactify string theory, this provides a direct method to compute the spacetime Kähler potential of certain moduli (e.g., vector multiplet moduli in type IIA), exactly in α′. We compute these quantities for the quintic and for Rødland’s Pfaffian Calabi–Yau threefold and find agreement with existing results in the literature. We then apply our methods to a codimension four determinantal Calabi–Yau threefold in
P
7
, recently given a nonabelian gauge theory description by the present authors, for which no mirror Calabi–Yau is currently known. We derive predictions for its Gromov–Witten invariants and verify that our predictions satisfy nontrivial geometric checks.
We study knots in 3d Chern-Simons theory with complex gauge group SL ( N , C ) , in the context of its relation with 3d = 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 M ˆ . We identify such defects in various corners of the 3d-3d correspondence, namely in 3d SL ( N , C ) CS theory, in 3d = 2 theory, in 5d = 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 1, which contains more details and more results.
Beijing Lectures on the Grade Restriction Rule Eager, Richard; Hori, Kentaro; Knapp, Johanna ...
Chinese annals of mathematics. Serie B,
07/2017, Letnik:
38, Številka:
4
Journal Article
Recenzirano
The authors describe the relationships between categories of B-branes in dif- ferent phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model ...proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rcdland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.
We investigate aspects of holographic duals to time-like warped
AdS
3
space-times — which include Gödel’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 world sheet analysis.
We develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi–Yau threefold. The problem is approached by studying framed 3d–5d ...wall-crossing in the presence of a single M5 brane wrapping a special Lagrangian submanifold
L
. The spectrum of 3d–5d BPS states is encoded by the geometry of the manifold of vacua of the 3d–5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. For the simplest Calabi–Yau,
C
3
we reproduce the count of 5d BPS states and match predictions of 3d
t
t
∗
geometry for the count of 3d–5d BPS states. We comment on applications of our construction to the study of enumerative invariants of toric Calabi–Yau threefolds.
Aspects of defects in 3d-3d correspondence Gang, Dongmin; Kim, Nakwoo; Romo, Mauricio ...
The journal of high energy physics,
10/2016, Letnik:
2016, Številka:
10
Journal Article
Recenzirano
Odprti dostop
A
bstract
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
S
L
N
ℂ
) on
M
and a 3d
N
=
2
theory
T
N
M
. We study 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
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, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when
N >
2. We also highlight the non-Abelian description of the 3d
N
=
2
T
N
M
theory with defect included, when such a description is available. This paper is a companion to our shorter paper 1, which summarizes our main results.
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