The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.
Eisenstein Series and String Thresholds
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abstract
We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.
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Higher-derivative corrections explicitly break all hidden symmetry enhancements in the three-dimensional reductions of non-maximal supergravities.
Under a duality symmetry assumption, minimal supergravity coupled to two vector multiplets in D=8 is uniquely fixed in the BPS sector by anomaly cancellation, uplifts, and gauge enhancement.
Wormhole effects in theories with imaginary massless scalars set an upper limit on analytic continuation of couplings to imaginary values, with string theory examples showing the low-energy theory breaks down at or before this bound.
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Taxonomy of Instanton Corrections in Infinite Distance Limits
The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.
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Symmetries of non-maximal supergravities with higher-derivative corrections
Higher-derivative corrections explicitly break all hidden symmetry enhancements in the three-dimensional reductions of non-maximal supergravities.
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Uniqueness of D=8 minimal supergravity with two vector multiplets
Under a duality symmetry assumption, minimal supergravity coupled to two vector multiplets in D=8 is uniquely fixed in the BPS sector by anomaly cancellation, uplifts, and gauge enhancement.
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Wormholes and the imaginary distance bound
Wormhole effects in theories with imaginary massless scalars set an upper limit on analytic continuation of couplings to imaginary values, with string theory examples showing the low-energy theory breaks down at or before this bound.