TY - JOUR

T1 - Infinite distances in field space and massless towers of states

AU - Grimm, Thomas W.

AU - Palti, Eran

AU - Valenzuela, Irene

PY - 2018/8/1

Y1 - 2018/8/1

N2 - It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space of Calabi-Yau manifolds is a good testing ground for this conjecture since it is known to encode quantum gravity physics. We study infinite distances in this setting and present new evidence for the above conjecture. Points in moduli space which are at infinite proper distance along any path are characterised by an infinite order monodromy matrix. We utilise the nilpotent orbit theorem to show that for a large class of such points the monodromy matrix generates an infinite orbit within the spectrum of BPS states. We identify an infinite tower of states with this orbit. Further, the theorem gives the local metric on the moduli space which can be used to show that the mass of the states decreases exponentially fast upon approaching the point. We also propose a reason for why infinite distances are related to infinite towers of states. Specifically, we present evidence that the infinite distance itself is an emergent quantum phenomenon induced by integrating out at one-loop the states that become massless. Concretely, we show that the behaviour of the field space metric upon approaching infinite distance can be recovered from integrating out the BPS states. Similarly, at infinite distance the gauge couplings of closed-string Abelian gauge symmetries vanish in a way which can be matched onto integrating out the infinite tower of charged BPS states. This presents evidence towards the idea that also the gauge theory weak-coupling limit can be thought of as emergent.

AB - It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space of Calabi-Yau manifolds is a good testing ground for this conjecture since it is known to encode quantum gravity physics. We study infinite distances in this setting and present new evidence for the above conjecture. Points in moduli space which are at infinite proper distance along any path are characterised by an infinite order monodromy matrix. We utilise the nilpotent orbit theorem to show that for a large class of such points the monodromy matrix generates an infinite orbit within the spectrum of BPS states. We identify an infinite tower of states with this orbit. Further, the theorem gives the local metric on the moduli space which can be used to show that the mass of the states decreases exponentially fast upon approaching the point. We also propose a reason for why infinite distances are related to infinite towers of states. Specifically, we present evidence that the infinite distance itself is an emergent quantum phenomenon induced by integrating out at one-loop the states that become massless. Concretely, we show that the behaviour of the field space metric upon approaching infinite distance can be recovered from integrating out the BPS states. Similarly, at infinite distance the gauge couplings of closed-string Abelian gauge symmetries vanish in a way which can be matched onto integrating out the infinite tower of charged BPS states. This presents evidence towards the idea that also the gauge theory weak-coupling limit can be thought of as emergent.

KW - D-branes

KW - Differential and Algebraic Geometry

KW - Effective Field Theories

KW - Superstring Vacua

UR - http://www.scopus.com/inward/record.url?scp=85052212816&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2018)143

DO - 10.1007/JHEP08(2018)143

M3 - Article

AN - SCOPUS:85052212816

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 8

M1 - 143

ER -