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 <math>\begin{align}   & \left\{ \begin{align}   & m{\alpha }'\tau \hbar \varepsilon \mu \alpha \mathbf{T}ic\varsigma  \\   & \text{      }\And  \\   & \text{  }\mathsf{\mathcal{P}}\pi y\sigma \mathbf{I}\subset \mathbf{S} \\  \end{align} \right\} \\   & \text{    }Wikia \\  \end{align}</math>

S-Duality

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String Theory
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All Roads Lead to String Theory (Polchinski)
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
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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
AdS CFT
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
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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).

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