Interview: Andreas Braun

Nolan Fitzpatrick: When physicists say that g2 manifolds allow for 1/8 the original supersymmetry, what does this really mean?

Andreas Braun: 11D supergravity has 32 supercharges (= independent generators of supersymmetry transformations), and 4 linear combinations remain unbroken when spacetime is the product of a G2 manifold times R^{1,3}. This is 1/8. 4 supercharges in 4D is what people usually call 4D N=1 supersymmetry.

Nolan Fitzpatrick: How exactly are we left with the realistic N=1 supersymmetry?

Andreas Braun: That depends what you mean by realistic. But besides gravity you can get gauge theories, charged matter, Yukawa couplings. The details of how well this is understood and how much has been achieved is a rather long story.

Nolan Fitzpatrick: Why, as Peter Horava notes, are we unable to derive realistic 4-dimensional physics from models of compactification that involve g2 manifolds?

Andreas Braun: I think it is far from clear that one can conclude such a thing. More generally, I think the challenges and possibilities are more or less the same for all string constructions of (realistic) 4D N=1 vacua if you start asking detailed questions.

Nolan Fitzpatrick: g2 manifolds,a 7-dimensional Riemannian manifolds. Thus, they have an odd number of dimensions and do not meet the requirements for being complex, like Calabi-yau. Why does this make g2 manifolds harder to work with?

Andreas Braun: Complex algebraic geometry is 'easy' and allows you to write down LOTs of examples of CY manifolds explicitly. There is no such technique available for G2 that we know of.

Nolan Fitzpatrick: What else is there to be learned about g2 manifolds?

Andreas Braun: A lot of things are still too difficult to describe and a lot of things one would like to compute we don't know how to tackle. Coming back to my answer in 3) the same can be said about other constructions of 4D N=1 vacua in string theory.

A very short wishlist for G2 is

- explicit construction of large classes/geometrical engineering of

chiral gauge theories in compact models

- detailed description of their moduli spaces

- finding associative submanifolds/non-perturbative corrections

Nolan Fitzpatrick: What do you think is the next step for g2 manifolds? For example, physicists such as Edward Witten and Shing-Tung Yau have attempted to construct something like the Calabi conjecture for g2 manifolds, however, have not gotten very far.

Andreas Braun: My guess is that a statement such as Calabi's conjecture does not hold in general for G2s, but there are certainly specific classes in which something similar holds. My best bet for progress is to continue using string dualities to better understand G2 manifolds.