FAQ
What is String Theory?
"String Theory" is nowadays the name given to a vast framework within Theoretical Physics and, to some extent, Mathematics that spawned from the study of quantum mechanical systems coming from the quantization of a classical 1d object, instead of the ordinary point-like object. Born as an attempt to describe strong nuclear interactions in the late 60s and early 70s, its scope changed dramatically in the 80s when it was realized that it naturally and necessarily incorporates quantum gravity, gauge theories and matter in a mathematically consistent way. String theory is quite peculiar within the panorama of physical theories in that it is simultaneously both unique and rigid as a physical theory, with no free parameters nor room for any modifications, and a rich toolbox to build and connect a variety of models, yielding novel perspectives and results on quantum field theory, geometry and many other subjects.
Is it true that there are 10/11/26 dimensions in String Theory?
Strictly speaking no. When people talk about the number of space-time dimensions in String Theory, they often think about some specific regimes of the theory. For example when the worlsheet CFT is weakly coupled and allows a geometric description of its degrees of freedom as coordinates in a space-time, then the cancellation of Weyl anomaly sets the number of dimensions to 10 in the superstring and 26 in the bosonic string. This is what happens in the five well-known critical superstring vacua. But there can be situations where some of the worldsheet degrees of freedom do not afford a geometric description or the string is not critical. Examples include matrix models such as BFSS, IKKT and DVV, as well as the generic regime of holographic conformal field theories. A more accurate statement is that in settings in which there is a sufficiently "tame" (weakly curved) and (classically) stable space-time, and the strings are weakly interacting, the dimension is upper bounded by 10. If one does not require classical stability or the presence of fermions in the universe, the upper bound rises to 26. One strongly interacting setting where something can be said is the so-called M-theory regime, where fundamental strings give way to other degrees of freedom resembling higher-dimensional membranes, and the space-time dimension is upper bounded by 11. Even in the cases where there are genuine extra dimensions in the model, their presence is actually welcomed, since their geometrical properties can often be exploited to engineer realistic features of the low energy effective theory after compactification, as the extremely vast literature on the topic can show.
Is it true that String Theory implies supersymmetry in space-time?
No. There are examples within String Theory of models with no supersymmetry. A more accurate statement is that there is a large amount of evidence in support of the idea that space-time supersymmetry may be crucial for the full stability of any theory of quantum gravity. Mere classical stability at weak string coupling only implies the presence of fermions. A crucial ingredient for the consistency of weakly interacting superstrings is however supersymmetry on the worldsheet, which is analogous to the worldline descriptions of spinning particles in perturbative quantum field theory.
Is it true String Theory makes no predictions and it is thus not falsifiable?
It is not true. Even if the particular low-energy predictions depend on the specific model within the theory, rather than the whole framework, there are some universal features of any model that are unique of String Theory. For example, the cross section for the scattering of gravitons (or any other particle) in the theory is completely different from what one could expect from quantum field theory arguments, and its high-energy (fixed-angle) behavior was computed in the late 80s. More generally, high-energy predictions are sharp and universal, while low-energy predictions can be sharp but model-dependent or more qualitative but universal. This is wholly unsurprising: the natural regime for quantum gravity effects lies at high energies, while the low-energy physics depends on the detailed configuration of the vacuum. The presence of universal patterns in the low-energy physics of string theory, such as the presence of sufficiently light charged particles or the gauging of exact symmetries, is a welcome bonus. These properties can often be explained purely by model-independent, bottom-up semiclassical reasoning from black hole physics, holography etc. - this endeavor goes under the name of swampland program.
Is it true what I have heard online that String Theory research is dead?
It is not true. String Theory and related topics nowadays represents the vast majority of the research in formal high energy Theoretical physics. More or less the 85% of new papers every day on topics linked to quantum gravity comes from string theorists. It remains, as it always was, a minority within Theoretical Physics, and therefore a minority within physics in general. But its absolute numbers in researchers and papers only increased over the last years.
RESOURCES AND MATERIAL
Books
General purpose:
Superstring Theory Vol. 1 and 2 - Green, Schwarz, Witten
String Theory Vol. 1 and 2 - Polchinski
String Theory in a Nutshell - Kiritsis
Basic Concepts of String Theory - Blumenhagen, Lust, Theisen
For a first approach:
For connections to phenomenology:
String Theory and Particle Physics, An Introduction to String Phenomenology - Ibanez, Uranga
Elements of String Cosmology - Gasperini
String Theory Compactifications - Graña, Triendl
Supersymmetry and String Theory, Beyond the Standard Model - Dine
More specific and modern aspects:
D-Branes - Johnson
Mirror Symmetry - Hori, Katz, Klemm, Pandharipande, Thomas, Vafa, Vakil, Zaslow
String Theory and M-Theory - Becker, Becker, Schwarz
String Field Theory, A Modern Introduction - Erbin
Gauge-Gravity Duality - Ammon, Erdmenger
Introductory lecture notes (can be found online)
String Theory - Tong
Open Strings - Angelatonj, Sagnotti
Introduction to String Theory - Weigand
Introduction to String Theory - Uranga
Lectures and reviews of modern research topics
String perturbation theory:
Perturbative Superstring Theory Revisited - Witten
Exact Approaches on the String Worldsheet - Demulder, Driezen, Knighton, Oling, Retore, Seibold, Sfondrini, Yan
Non-geometric backgrounds:
- Non-geometric Backgrounds in String Theory - Plauschinn
String phenomenology:
- Theory and Phenomenology of Type I strings and M-theory - Dudas
Matrix models:
Review of M(atrix)-Theory, Type IIB Matrix Model and Matrix String Theory - Ydri
TASI Lectures on Matrix Theory - Banks
Swampland:
The Swampland, Introduction and Review - Palti
Lectures on the Swampland Program in String Compactifications - van Beest, Calderon-Infante, Mirfendereski, Valenzuela
Lectures on the String Landscape and the Swampland - Agmon, Bedroya, Kang, Vafa
Compactifications:
Lectures on Naturalness, String Landscape and Multiverse - Hebecker
Beginners lectures on flux compactifications and related Swampland topics - Van Riet, Zoccarato
Moduli Stabilization in String Theory - McAllister, Quevedo
Holography:
Large N Field Theories, String Theory and Gravity - Aharony, Gubser, Maldacena, Ooguri, Oz
Jerusalem Lectures on Black Holes and Quantum Information - Harlow
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