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CHAPTER 11 Type II String Theories
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Type II B Theory
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We have seen that type II A theory is characterized by opposite chirality. Type II B theory is characterized by the same chirality. That is, for a state R1 R2 R1 and R2 will have the same chirality. The left and right movers will have the same GSO projection:
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The spinor eld satis es
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11S a = S a
(11.28)
b 1/ 2 0
right NS
b 1/ 2 0
left NS
right R
also have the same chirality.
The Massless Spectrum of Different Sectors
We conclude the chapter by noting the spectrum of states seen in the different sectors, and describing how these are different in type II A and type II B string theories. For those with a background in differential geometry or general relativity, forms are odd in type II A theory and even in type II B theory.
THE |NS |NS SECTOR
Type II A and type II B string theories have the same NS-NS sector. The spectrum of states in the NS-NS sector is A scalar eld which is the dilaton described in the last chapter (1 state) An antisymmetric gauge eld with 28 states A symmetric traceless rank two tensor G (this is the graviton) with 35 states
String Theory Demysti ed
THE |NS |R , |R |NS SECTOR
The states in these sectors are superpartners of the dilaton and the graviton. Type II A and type II B theories have the same states, but the states NS R , R NS each have the same chirality in type II B theory and have the opposite chirality in type II A theory. The states are The dilatino, the spin-1/2 superpartner of the dilaton, with 28 states. The gravitino, the spin-3/2 fermion which is the superpartner of the graviton. For type II A theory the 2 gravitinos have opposite chirality.
THE |R |R SECTOR
These are boson states formed from the tensor product of two Majorana-Weyl spinors. In type II A theory the left and right states have opposite chirality, while in type II B theory they have the same chirality. For type II A theory, there are two states: A vector gauge eld A 3-form gauge eld (see Relativity Demysti ed for a description of forms) In type II B theory the states are A scalar eld A two-form gauge eld A four-form gauge eld
Summary
In this chapter, we have summarized the states of type II A and type II B string theories, which are based on the R and NS sectors first introduced in Chap. 7. Type II A theory consists of states that are tensor products of states with opposite chiralities, while type II B theory consists of states that are tensor products of states with the same chiralities. This results in different particle states. These theories predict the existence of superpartners that have not yet been observed in nature.
CHAPTER 11 Type II String Theories
Quiz
1. Type II string theories: (a) Include only open strings (b) Include open and closed strings (c) Include only closed strings (d) Include open strings only if they are oriented 2. States in the NS sector can be described in space-time as: (a) NS sector states must be combined with R sector states to give space-time fermions, otherwise they do not describe states in space-time. (b) Space-time bosons. (c) Space-time fermions. (d) Space-time bosons for oriented strings, space-time fermions for unoriented strings. 3. The spin eld operator S a = e i / 2 e i / 2 is what type of spinor How many components does it have in general
(a) SO(10), 16 components (b) SO(10), 32 components (c) SO(32), 10 components (d) SO(10), 10 components 4. The superpartner states in the NS R , R NS sectors include: (a) The dilatino and the gravitino. For type II A theory the 2 gravitinos have opposite chirality. (b) The dilatino and the gravitino. For type II A theory the 2 gravitinos have the same chirality. (c) The dilatino and the gravitino. For type II A theory the 2 dilatinos have opposite chirality. (d) The dilatino and the gravitino. For type II A theory the 2 dilatinos have the same chirality.
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