# Gravitational wave and string theory

I'm new to physics and have been reading about fundamental and textbook physics text, which is the Young & Freedman University Physics (good book).

I'm little skeptical towards string theory as it is presented and explained now.

I also listen to lectures of Leonard Susskind, who is one of the founders of string theory and a very highly regarded physicist, and he says in this YouTube video (published on Jan 27, 2016, before the LIGO announcement) at 9:32 that

"If these gravitational waves are seen in the cosmic microwave background, I think that would be very very hard to digest for a string theorist."

Why does he say that gravitational wave and string theory cannot be reconciled? Is there a contradiction between gravitational wave and string theory? Is string theory practically dead because of gravitational wave and the inability of super colliders to find supersymmetry? What makes gravitational wave not work with string theory? I'm not looking for deep technical answer, but a little pointer on this topic.

• Gravitational waves, in general, present no problem to string theory. It's specifically gravitational waves in the CMBR that present a problem because of the limit they would impose on the inflation field. See this paper – lemon May 22 '16 at 15:51

The graviton in string theory is an aspect of closed heterotic strings. The reason for closed strings is that there are two independent modes, called right and left oriented modes. This is in contrast to the open string where modes in both directions are the same, being of course reflected back and forth. We may think of these modes as $a, a^\dagger$ and $b, b^\dagger$. The string expanded in these modes constructs a Lagrangian with the operator products $a^\dagger b^\dagger$, $ab^\dagger$, $a^\dagger b$ and $ab$. The first and the last of these can be thought of as products of spin-1 gauge field operators that form a spin-2 field. These compositions give the gravitons field. The other two terms correspond to a product with a net zero angular momentum, which is interpreted as $m = 0$ case for the angular momentum operator projected on the $z$-axis. This corresponds to a gravity wave with mass, which is generally ignored.
This construction is compatible with the construction of the gravi-electric and magnetic fields. For the Weyl tensor $C_{\alpha\mu\beta\nu}$ gravi-electric field is $$E_{\mu\nu} = C_{\alpha\mu\beta\nu}U^\alpha U^\beta$$ and the magnetic field as $$B_{\mu\nu} = *C_{\alpha\mu\beta\nu}U^\alpha U^\beta,$$ for $*$ the Hodge dual-star operator. For the Petrov type N solution these electric/magnetic field tensors are physically then composed of gravitons seen in the last paragraph. With Typoe II and III Petrov solution types, which are physically sort of self-bound gravity waves or curvatures, we have a sort of induced mass from self-interaction.