Golden	 Jubilee	 of	 String	 Theory	 Strings	 2018
Okinawa,	 Japan	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 What is perturbative string theory?

Xi	 YinHarvard	 University

Three facets of weakly coupled strings
1. The spacetime S-matrix[Veneziano ’68, …, Caron-Huot, Komargodski, Sever, Zhiboedov, ’16, …]

2. The effective string[Nambu-Goto, Green-Schwarz ’81, … Polchinski, Strominger ’91,
Dubovsky, Flauger, Gorbenko ’12, Aharony, Komargodski ’13,Hellerman, Swanson ’13, …]

3. The worldsheet CFT[Polyakov ’81, … Friedan, Martinec, Shenker ’85, …, Zwiebach ’92,…, Berkovits, Vafa, Witten ’99, Berkovits ’00, …, Sen ’14, …]

Weakly coupled relativistic string theories are ubiquitous, e.g.
flux strings in large N confining gauge theories. Excitations
are trapped on the string in the free-string/infinite-N limit.
In critical string theories, excitations on a long string happen
to be integrable.
A more general relativistic string … may be embeddable incritical string theory in a nontrivially warped background?

[Maldacena ’98, Witten ’98,Aharony, Karzbrun ’09, …]

… or bootstrapped through the 1+1 dim S-matrix on a longstring? [Paulos, Penedones, Toledo, van Rees, Vieira, ’16]
Note: not a local 1+1 d QFT in static gauge.

UV/IR connection, reminiscent of gravity S-matrix …
[Dubovsky, Gorbenko ’15, Dubovsky ’18]

Standard recipe for UV completion of the effective theory of
weakly coupled strings: worldsheet CFT with BRST symmetry.
Implicit assumption: locality on the worldsheet (in theconformal gauge).
But, is a local worldsheet CFT necessary? Or is it just an
accident in critical string theory?
A clue: superstrings in RR flux background.

It is often asserted that NSR formalism does not apply in
RR flux background.
Not a problem in closed superstring field theory based on
NSR formalism and PCOs. [Pius, coffee break]Can also describe RR flux background as deformation ofworldsheet CFT in NSR formalism. [Berenstein, Leigh ’99]

Insert into the worldsheet correlator

Cancelation of Weyl anomaly due to colliding RR vertex
operators by NS-NS operators (that would have been off-shellby themselves) leads to supergravity equations involving RRfluxes. [Berenstein, Leigh ’99]
Can compute correction to string spectrum, agrees withexpectation in pp-wave and AdS3xS3 with RR-flux.
[Cho, Collier, XY, W.I.P.]

This looks like a nonlocal deformation of the worldsheet
CFT.

Perhaps the worldsheet nonlocality in RR flux background iscircumvented in pure spinor formalism, but this is far fromobvious, as interacting ghost systems are hard to define
quantumly. [Berkovits, Vafa, Witten, ’99, Berkovits ’00, ’02, …]
A cautionary tale: Liouville CFT cannot be thought of as aperturbation of linear dilaton theory.
Doing so in the early 90s (pre-DOZZ era) has led to a great dealof confusion in the study of c=1 string theory, much of which isresolved when the correct CFT results are applied.
[Balthazar, Rodriguez, XY, ’17 + W.I.P.]

Interacting ghost systems resemble non-unitary Liouvilletheories… rule of quantization a priori unclear.

Conclusion: there is much to be understood on theworldsheet.

Hope for the future: a more general framework for
UV completion of effective strings.