## FANDOM

118 Pages

String Theory
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
String
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
BPS
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
D-Brane
S-Duality
Horava-Witten String Theory
M-Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

Like T-Duality, S-Duality is a duality, or equivalence, between theories. Unlike T-Duality, S-Duality is not a purely stringy concept as it also appears in Quantum Field Theorys. S-Duality is useful because equates a Strongly-Coupled theory with a Weakly-Coupled theory. I.e. it equates a theory with coupling constant $\frac1{g_s}$ with a theory with coupling constant ${g}_{s}$.

## S-Duality and the DilatonEdit this section

In String Theory, the coupling constant is related to the Dilaton Field:

$g_s=\langle e^\Phi \rangle$

Negating the Dilaton Field is equivalent to inverting the coupling constant:

$\frac1{g_s}=\frac1{\langle e^\Phi\rangle}=e^{-\Phi}$

Therefore, S-Duality negates the Dilaton Field, in a similar way as to how T-Duality negates the bosonic and fermionic fields, ; $X^\mu$ and $\psi^\mu$/.

## S-Duality in String TheoryEdit this section

In String Theory, analysing the massless fields and mass spectra of String Theoryies shows that Type I String Theory is S-Dual to Type HO String Theory and Type IIB String Theory is S-Dual to itself. More specifically, Type I String Theory with D-Branes instead of F1-Strings is S-Dual to Type HO String Theory and Type IIB String Theory with D-Branes instead of F1-Strings is S-Dual to itself (but with F1 Strings).