The three dimensional = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various = 2 U(N) Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.

https://iopscience.iop.org/article/10.1088/1126-6708/2007/08/056/pdf

Notes on superconformal Chern-Simons-Matter theories

We provide a significant extension of the twisted connected sum construction of G_2-manifolds, i.e. Riemannian 7-manifolds with holonomy group G_2, first developed by Kovalev; along the way we address some foundational questions at the heart of the twisted connected sum construction. Some of the main contributions of the paper are: 
(i) We correct, clarify and extend several aspects of the K3 "matching problem" that occurs as a key step in the twisted connected sum construction. 
(ii) We show that the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds (a subclass of weak Fano 3-folds) can be used as components in the twisted connected sum construction. 
(iii) We construct many new topological types of compact G_2-manifolds by applying the twisted connected sum to asymptotically Calabi-Yau 3-folds of semi-Fano type studied in arXiv:1206.2277. 
(iv) We obtain much more precise topological information about twisted connected sum G_2-manifolds; one application is the determination for the first time of the diffeomorphism type of many compact G_2-manifolds. 
(v) We describe "geometric transitions" between G_2-metrics on different 7-manifolds mimicking "flopping" behaviour among semi-Fano 3-folds and "conifold transitions" between Fano and semi-Fano 3-folds. 
(vi) We construct many G_2-manifolds that contain rigid compact associative 3-folds. 
(vii) We prove that many smooth 2-connected 7-manifolds can be realised as twisted connected sums in numerous ways; by varying the building blocks matched we can vary the number of rigid associative 3-folds constructed therein. This leads to speculation that the moduli space of G_2-metrics on a given 7-manifold may consist of many different connected components.

/pdf/g-2-manifolds-and-associative-submanifolds-via-semi-fano-3-4mfdeejsd7.pdf

G_2-manifolds and associative submanifolds via semi-Fano 3-folds

We construct many new topological types of compact G 2 -manifolds, that is, Riemannian 7 -manifolds with holonomy group G 2 . To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class of asymptotically cylindrical Calabi–Yau 3 -folds built from semi-Fano 3 -folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 7 -manifolds completely; we find that many 2 -connected 7 -manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G 2 -metrics. Many of the G 2 -manifolds we construct contain compact rigid associative 3 -folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/calibrated submanifolds) approach to defining deformation invariants of G 2 -metrics. By varying the semi-Fanos used to build different G 2 -metrics on the same 7 -manifold we can change the number of rigid associative 3 -folds we produce.

/pdf/g2-manifolds-and-associative-submanifolds-via-semi-fano-3-4rd9cid3jc.pdf

G2-manifolds and associative submanifolds via semi-Fano 3-folds

If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all nongravitational physics: the standard model. But despite this monumental achievement there is a clear sense of disappointment: many questions remain unanswered. Remarkably, most unanswered questions could just be environmental, and disturbingly to some the existence of life may depend on that environment. Meanwhile there has been increasing evidence that the seemingly ideal candidate for answering these questions, string theory, gives an answer few people initially expected: a large ``landscape'' of possibilities that can be realized in a multiverse and populated by eternal inflation. At the interface of ``bottom-up'' and ``top-down'' physics, a discussion of anthropic arguments becomes unavoidable. Developments in this area are reviewed, focusing especially on the last decade.

/pdf/life-at-the-interface-of-particle-physics-and-string-theory-14p8c5yb17.pdf

Life at the Interface of Particle Physics and String Theory

We analyze the cosmological signatures visible to an observer in a Coleman-de Luccia bubble when another such bubble collides with it. We use a gluing procedure to generalize the results of Freivogel, Horowitz and Shenker to the case of a general cosmological constant in each bubble and study the resulting spacetimes. The collision breaks the isotropy and homogeneity of the bubble universe and provides a cosmological 'axis of evil' which can affect the cosmic microwave background in several unique and potentially detectable ways. Unlike more conventional perturbations to the inflationary initial state, these signatures can survive even relatively long periods of inflation. In addition, we find that for a given collision the observers in the bubble with smaller cosmological constant are safest from collisions with domain walls, possibly providing another anthropic selection principle for small positive vacuum energy.

When Worlds Collide

We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's ``sky,'' finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky. After a qualitative discussion of the physics involved in collisions between arbitrary bubbles, we evaluate the implications of our results, and outline possible detectable effects. In an optimistic sense, then, the present paper constitutes a first step in an assessment of the possible effects of other bubble universes on the cosmic microwave background and other observables.

Towards observable signatures of other bubble universes

We construct new topological theories related to sigma models whose target space is a seven-dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six-dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin’s functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G2 manifolds. When the seven-dimensional topological twist is applied to the product of a Calabi–Yau manifold and a circle, the result is an interesting combination of the six-dimensional A and B models.

https://projecteuclid.org/download/pdf_1/euclid.atmp/1210083226

The Topological G 2 String

We argue that the Penrose limit of a general string background is a generalization of the Seiberg-Sen limit describing M(atrix) theory as the DLCQ of M theory in flat space. The BMN theory of type IIB strings on the maximally supersymmetric pp-wave background is understood as the exact analogue of the BFSS M(atrix) theory, namely, a DLCQ of IIB string theory on $AdS_5 \times S^5$ in the limit of infinite longitudinal momentum. This point of view is used to explain some features of the BMN duality.

Assaf Shomer

Papers

Towards observable signatures of other bubble universes

The Topological G 2 String

Penrose limit and discrete light cone quantization of string theory