In string theory the term swampland had been introduced (Vafa 05) to publicly highlight the basic fact that many effective quantum field theory vacua will not admit a UV-completion to a string theory vacuum, hence that admitting a completion to a string theory vacuum is a strong constraint, hence that string theory predicts many more conditions to be satisfied by gauge groups, field content and coupling constants than predicted by plain quantum field theory.
The terminology was motivated since the collection of string theory vacua had previously come to be called the landscape of string theory vacua. The idea is to imagine the remaining EFTs not “in” this landscape to form a space “away from the landscape”, whence the colorful imagery of a swampland.
More in detail, there is supposedly a map
that takes string theory vacua to their low-energy approximation by vacua of effective quantum field theories. One way to possibly formalize this is to take the point-particle limit (ppl) of 2d SCFTs to obtain spectral triples (as discussed at 2-spectral triple) taking string worldsheets to Feynman diagrams:
graphics grabbed from Schubert 96
Then with language of homological algebra or more generally of category theory we may begin to formalize the situation as follows:
the domain of (1) is the landscape of string theory vacua;
the image of (1) is the landscape of corresponding eQFTs that admit stringy UV-completion;
the kernel of (1), or more generally its fiber over any EFT, is the space of different choices of stringy UV-completion of the same effective quantum field theory.
Making this fully precise requires saying more about what the domain and codomain in (1) actually are, and in which ambient category (they will be some kind of moduli stacks in an ambient (∞,1)-category which may not quite be stable, whence “cokernel” may need to be interpreted in a non-abelian sense; but such details don’t change the general idea here).
For example, part of what it means to specify a string theory vacuum is to declare the D-brane charge contained in this vacuum (subject to RR-field tadpole cancellation against O-plane-charges). In actual string theory this RR-field charge is supposed to be (see there) a cocycle in some flavour of topological K-theory (twisted equivariant differential KR-theory), while its image in the underlying effective field theory is in the corresponding flavour of ordinary cohomology/de Rham cohomology. The map that relates the two incarnations of RR-field charge is the Chern character, which is what formalizes the map (1) in in the D-brane charge “sector” of the theory
The Chern character in general does have non-trivial cokernel (“swampland RR-fields”) and kernel (choices of UV-completion of the effective RR-fields). In fact it fits not just in a short exact sequence, but in the differential cohomology hexagon (see there for more) of K-theory.
In contrast to this example, the literature on the “swampland” phenomenon is currently dominated by informal hand-wavy arguments. Starting with Ooguri-Vafa 06 is an attempt to guess semi-precise rules-of-thumb for recognizing EFTs in the swampland, now known as the swampland conjectures. Motivated by the re-opening of the question whether de Sitter spacetime actually appears in string theory vacua or not (Danielsson-van Riet 18), these swampland conjecture currently revolve around bounds on the cosmological constant in relation to scalar fields in the theory.
The terminology originates with
Comprehensive review is in:
Further discussion includes
Hirosi Ooguri, Cumrun Vafa, On the Geometry of the String Landscape and the Swampland, Nucl.Phys.B766:21-33, 2007 (arXiv:hep-th/0605264)
T. Daniel Brennan, Federico Carta, Cumrun Vafa, The String Landscape, the Swampland, and the Missing Corner (arXiv:1711.00864)
Ben Heidenreich, Matthew Reece, Tom Rudelius, Emergence and the Swampland Conjectures (arXiv:1802.08698)
See also
Beware that the landscape literature is presently completly dominated by non-rigorous hand-wavy string phenomenology.
One question is if de Sitter spacetime-vacua belong to the swampland or not:
Ulf Danielsson, Thomas Van Riet, What if string theory has no de Sitter vacua?, International Journal of Modern Physics D, Vol. 27, No. 12, 1830007 (2018) (arXiv:1804.01120, doi:10.1142/S0218271818300070)
Thomas Van Riet, Is dS space in the Swampland, talk at StringPheno18 (pdf slides)
Thomas Van Riet, Status of KKLT, talk at Simons summer workshop 2018 (recording)
Georges Obied, Hirosi Ooguri, Lev Spodyneiko, Cumrun Vafa, De Sitter Space and the Swampland (arXiv:1806.08362)
Prateek Agrawal, Georges Obied, Paul Steinhardt, Cumrun Vafa, On the Cosmological Implications of the String Swampland (arXiv:1806.09718)
Cumrun Vafa, Cosmology and the String Swampland, talk at Strings 2018 (pdf slides, recording)
Frederik Denef, Arthur Hebecker, Timm Wrase, The dS swampland conjecture and the Higgs potential (arXiv:1807.06581)
Ulf Danielsson, The quantum swampland (arXiv:1809.04512)
(argues that the issue with stringy de Sitter moduli stabilization raised in Sethi 17 is related to the de Sitter instability seen in QFT, according to the references above)
Last revised on July 10, 2019 at 17:19:00. See the history of this page for a list of all contributions to it.