The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

The Swampland: Introduction and Review

The complete superconformal index for N=6 Chern–Simons theory

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of an ideal Fermi gas with a non-trivial, one-particle quantum Hamiltonian. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the WKB or semiclassical expansion of the quantum gas, and we show that, for several quiver Chern-Simons-matter theories, it is given by an Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas corresponds to a strong coupling expansion in type IIA theory, and it is dual to the genus expansion. This allows us to calculate explicitly non-perturbative effects due to D2-brane instantons in the AdS background.

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ABJM theory as a Fermi gas

The mere existence of six-dimensional supersymmetric ``$(2,0)$'' conformal field theories implies many deep, nonperturbative dualities within the landscape of four- and three- dimensional quantum field theories. All evidence for these $6D$ theories is indirect and they are intrinsically nonperturbative, defying a conventional (Lagrangian) definition. This paper pushes methods developed for two dimensions (``bootstrap'') to higher dimensions, exploiting symmetries and numerical methods to obtain, for the first time, concrete results for the spectrum, correlation functions, etc., of these mysterious theories, without resorting to simplifying limitations.

/pdf/the-2-0-superconformal-bootstrap-2zi0qfmvk2.pdf

The (2, 0) superconformal bootstrap

We study a three-dimensional = 3 U(N)k × U(N)−k Chern-Simons matter theory with flavour, corresponding to the = 6 Aharony-Bergman-Jafferis-Maldacena CSM theory coupled to 2Nf fundamental fields. The dual holographic description is given by the near-horizon geometry of N M2-branes at a particular hypertoric geometry 8. We explicitly construct the space 8 and match its isometries to the global symmetries of the field theory. We also discuss the model in the quenched approximation by embedding probe D6-branes in AdS4 × .

https://iopscience.iop.org/article/10.1088/1126-6708/2009/04/129/pdf

A note on the holography of Chern-Simons matter theories with flavour

We study mass-deformed N = 2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of ℂ2 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T2, which we calculate explicitly.

http://cds.cern.ch/record/1606035/files/arXiv:1310.1325.pdf

M-strings, Elliptic Genera and N=4 String Amplitudes

We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons terms induced by integrating out charged massive fields. The considered massive fields are spin-1/2 and spin-3/2 fermions, as well as complex two-forms with first order kinetic terms. Consistency with six-dimensional gravitational anomalies of (1, 0) and (2, 0) theories is shown by interpreting the massive fields as excited Kaluza-Klein modes in a circle compactification. The results are in accordance with the geometric predictions of the M-theory to F-theory duality as well as the comparison with an explicit one-loop computation in heterotic string theory compactified on K3 × S
 1.

https://link.springer.com/content/pdf/10.1007%2FJHEP07%282013%29043.pdf

One-loop Chern-Simons terms in five dimensions

With the aim to study six-dimensional (2, 0) superconformal theories with non-Abelian tensor multiplets we propose a five-dimensional superconformal action with eight supersymmetries for an infinite tower of non-Abelian vector, tensor and hypermultiplets. It describes the dynamics of the complete spectrum of the (2, 0) theories compactified on a circle coupled to an additional vector multiplet containing the circle radius and the Kaluza-Klein vector arising from the six-dimensional metric. All couplings are only given in terms of group theoretical constants and the Kaluza-Klein levels. After superconformal symmetry is reduced to Poincare supersymmetry we find a Kaluza-Klein inspired action coupling super-Yang-Mills theory to an infinite tower of massive non-Abelian tensors. We explore the possibility to restore sixteen supersymmetries by using techniques known from harmonic superspace. Namely, additional bosonic coordinates on a four-sphere are introduced to enhance the R-symmetry group. Maximally supersymmetric Yang-Mills theories and the Abelian (2, 0) tensor theories are recovered as special cases of our construction. Finally, we comment on the generation of an anomaly balancing Wess-Zumino term for the R-symmetry vector at one loop.

Non-Abelian tensor towers and (2,0) superconformal theories

We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons terms induced by integrating out charged massive fields. The considered massive fields are spin-1/2 and spin-3/2 fermions, as well as complex two-forms with first order kinetic terms. Consistency with six-dimensional gravitational anomalies of (1,0) and (2,0) theories is shown by interpreting the massive fields as excited Kaluza-Klein modes in a circle compactification. The results are in accordance with the geometric predictions of the M-theory to F-theory duality as well as the comparison with an explicit one-loop computation in heterotic string theory compactified on K3 x S^1.

Stefan Hohenegger

Papers

A note on the holography of Chern-Simons matter theories with flavour

M-strings, Elliptic Genera and N=4 String Amplitudes

One-loop Chern-Simons terms in five dimensions

Non-Abelian tensor towers and (2,0) superconformal theories

One-loop Chern-Simons terms in five dimensions