The EFT stringy viewpoint on large distances

Abstract

We observe a direct relation between the existence of fundamental axionic strings, dubbed EFT strings, and infinite distance limits in 4d $$ \mathcal{N} $$ N = 1 EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as RG flow of their couplings, and allows one to probe different regimes within the field space of the theory. We propose that any 4d EFT infinite distance limit can be realised as an EFT string flow. We show that along such limits the EFT string becomes asymptotically tensionless, and so the EFT eventually breaks down. This provides an upper bound for the maximal field range of an EFT with a finite cut-off, and reproduces the Swampland Distance Conjecture from a bottom-up perspective. Even if there are typically other towers of particles becoming light, we propose that the mass of the leading tower scales as m2 ∼ $$ \mathcal{T} $$ T w in Planck units, with $$ \mathcal{T} $$ T the EFT string tension and w a positive integer. Our results hold even in the presence of a non-trivial potential, as long as its energy scale remains well below the cut-off. We check both proposals for large classes of 4d $$ \mathcal{N} $$ N = 1 string compactifications, finding that only the values w = 1, 2, 3 are realised.

The Weak Gravity Conjecture and axion strings

“…This argument fits nicely not only with the Emergent String Conjecture of [7], but also with the Distant Axionic String Conjecture of [18,20]. The latter postulates that infinite distance limits in 4d N = 1 supersymmetric theories of quantum gravity can be viewed as RG flows into the core of an axion string.…”

“…However, the perspective of this paper suggests that in some ways Kaluza-Klein theory may be an exception to the rule, with theories of low-tension strings providing the more generic example of a weak-coupling limit. Our work has obvious connections to the Emergent String Conjecture of [7] and the Distant Axionic String Conjecture of [18,20]. It would be worthwhile to explore these connections further.…”

“…This scale, at which high-spin states must appear, is nothing other than the 5d Planck scale; indeed, this one-third scaling has appeared in past arguments relating WGC towers to emergence [3,49]. It is also an example of [20]'s m 2 ∝ T w scaling with w = 3. The axion strings of θ are simply the magnetic monopoles of the graviphoton in 5d, which can carry electric charge via the (5d version of the) Witten effect associated with the Chern-Simons coupling (3.4).…”

“…The charged modes include high-spin JHEP11(2021)004 states, and local QFT with a finite number of fields is no longer valid. Indeed, it has been proposed that these two options -the presence of extra dimensions as in Kaluza-Klein theory, or of low-tension strings -are the only possibilities for realizing a small-g gauge theory in quantum gravity [7], a claim (called the Emergent String Conjecture) supported by many studies of well-understood corners of the string landscape [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. (These studies relate the WGC to the more general Distance Conjecture regarding infinite-distance limits in quantum gravity [22][23][24][25].…”

“…To understand the relationship between the earlier conjectures, notice that the Emergent String Conjecture focuses on the tower of states that becomes light most quickly, which may be a Kaluza-Klein tower even when there is also a string becoming tensionless (at a slower rate). In such cases, [20] conjectured that the mass scale of the tower always relates to the axion string tension as m 2 ∝ T w , with w ∈ Z >0 . We will discuss such an example below.…”