## Tuesday, February 27, 2018

### Draining several parts of the swampland simutaneously

In 2005, my office was next to Cumrun Vafa's so I could watch him while plotting his plans to drain the swampland, more than a decade before Donald Trump (well, "drain the swamp" has been used for very different goals since the 19th century). His work preceded the main wave of the anti-stringy hysteria – that came in 2006 when two notorious cranks published their books – but I think it was at least partly motivated by various ludicrous claims about "unpredictive string theory".

He pointed out – and tried to clearly articulate and decorate with a new term – something that all string theorists always saw. The effective laws of physics that you may derive as long-distance approximations of string theory aren't just "any" or "generic" effective field theories. Effective field theories allow too many features that are prohibited in string theory. String theory seems to imply some extra conditions and regularities that couldn't have been derived by effective field theory itself.

These days, the Weak Gravity Conjecture (WGC), the first hep-th preprint of 2006, is probably the most well-known example of these swampland-like restrictions. Some people even know the term WGC while they're ignorant about the general concept of the swampland.

But WGC is just one type of general predictions that are special for string theory. Cumrun pointed out that the volume of moduli spaces seems to be finite in string theory – while effective field theories seemed to allow both finite and infinite volumes.

Also, the number of field species seems to be finite, like the ranks and dimensions of gauge groups. And in May 2006, Ooguri and Vafa discussed some general but characteristically stringy behavior of the particle spectrum near special points of the moduli space. The density grows with the mass in a certain way. I would add that the omnipresent "towers of states" in string theory have to be there because they're the precursors to the exponentially growing towers of black hole microstates in quantum gravity.

Among similar observations, we also find the observation that it's hard, to say the least, to realize "large scale inflation" within string theory. With canonically normalized kinetic terms for scalar fields, it seems hard to allow an inflaton to move by much more than one Planck mass. It seemed like string theory would prefer Guth's old inflation over Linde's new inflation.

In all of this business, the observed extra constraints were usually figured out by "experimentally watching" properties of string theory's vacua. But string theory is a consistent theory of quantum gravity and many of us find it likely that it's the only consistent theory of quantum gravity. So these stringy constraints may also be viewed as hypothetical restrictions that consistency of quantum gravity (a seemingly more general framework) imposes on effective field theories that may be incorporated.

More generally, seemingly non-stringy arguments may be constructed to argue that the conditions implied by string theory actually follow from the coherent unification of quantum mechanics and gravity. So far, all clear enough statements are consistent with the assumption that "string theory" and "consistent quantum gravity" are the same beast observed from different directions.

In the first hep-th preprint today,
Emergence and the Swampland Conjectures
Ben Heidenreich, Matthew Reece, and Tom Rudelius are trying to bring some order to these seemingly unrelated, chaotic observations about the "extra constraints" imposed by string theory. They derive the rich tower of light states from a new assumption they propose as a more fundamental one: the assumption that loop corrections drive both gravity and scalar interactions to the strong coupling at the same scale (well, this is a sort of a "soft unification" assumption and I will use that term for their assumption).

With this assumption, the collection of states that become light near a point of the moduli space automatically needs to be a "rich tower of states". The same "soft unification" assumption of theirs also seems to imply that the "large field inflation" should be prohibited.

These qualitative properties of string theory and/or quantum gravity should be understood increasingly well – including various logical relationships between seemingly independent assumptions of this sort. Along with some progress in the information loss paradox and entanglement/glue duality, a crisp new definition of string theory or quantum gravity could ultimately emerge in front of the eyes of someone whose thinking about the matters is simply clever.