Four Dimensional $\mathcal{N}=4$ SYM and the Swampland

Abstract

We consider supergravity theories with 16 supercharges in Minkowski space with dimensions $d>3$. We argue that there is an upper bound on the number of massless modes in such theories depending on $d$. In particular we show that the rank of the gauge symmetry group $G$ in $d$ dimensions is bounded by $r_G\le 26-d$. This in particular demonstrates that 4 dimensional $\mathcal{N}=4$ SYM theories with rank bigger than 22, despite being consistent and indeed finite before coupling to gravity, cannot be consistently coupled to $\mathcal{N}=4$ supergravity in Minkowski space and belong to the swampland. Our argument is based on the swampland conditions of completeness of spectrum of defects as well as a strong form of the distance conjecture and relies on unitarity as well as supersymmetry of the worldsheet theory of BPS strings. The results are compatible with known string constructions and provide further evidence for the string lamppost principle (SLP): that string theory lamppost seems to capture $all$ consistent quantum gravitational theories.

8 pages, v2: minor changes

References in corpus (5)

• On the Geometry of the String Landscape and the Swampland
• Global aspects of the space of 6D N = 1 supergravities
• Asymptotic Flux Compactifications and the Swampland
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory

Cited by in corpus (32)

• Lectures on the Swampland Program in String Compactifications
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Holo-ween
• The anomaly that was not meant IIB
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Special Geometry and the Swampland
• Exploring the landscape of CHL strings on T^d
• Taming the Landscape of Effective Theories
• Global anomalies in 8d supergravity
• New Supersymmetric String Theories from Discrete Theta Angles
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Looking for structure in the cobordism conjecture
• Type IIB flux compactifications with $h^{1,1}=0$
• Towards a complete classification of 6D supergravities
• Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape
• Swampland geometry and the gauge couplings
• Finiteness of 3D higher spin gravity Landscape
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Infinite distances in multicritical CFTs and higher-spin holography
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Consistency of eight-dimensional supergravities: Anomalies, Lattices and Counterterms
• A (strictly) contemporary perspective on trans-Planckian censorship
• Landscape of Narain CFTs
• Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles
• A unique coupling of the massive spin-2 field to supergravity
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape