Index

A-model, 163, 166, 176, 179, 180, 185

action, 169, 172

correlation function, 168–170, 189,

see also Gromov-Witten

invariant

fermionic symmetry of, see BRST

symmetry

observable, 169, 176

abelian group, 68

free, 70

homomorphism of, 69, 76

action, 136–137, 143, 146

bosonic string, see string theory,

bosonic, action

of A-model, see A-model, action

supersymmetric, 150, 151

symmetry of, 139, 141

continuous, 139

example of, 141

fermionic, 163

inﬁnitesimal, 140, 143

algebraic curve, 31

isomorphism of, 32

algebraic geometry, 9, 20

angular momentum, 141

antisymmetric product, 61, see also

wedge product

area form, 160, 171

arithmetic genus, 34

atlas, 50, 58, 60

B-model

correlation function, 177, 189

ball, 44, 45

Berezin integral, 149, 153, see also

fermionic integration

B´ ezout’s theorem, 16, 17, 19, 21, 22,

24, 41, 80–81, 193, 194, see also

enumerative geometry, in the

plane

big quantum cohomology, 191–196

product, 194

associativity of, 194–196

of

P1,

194–195

of

P2,

195–196

bosonic string action, see string

theory, bosonic, action

boundary, 54, 72

boundary operator, 71

branch point, 36, 38, 42

BRST cohomology, 166, 168

BRST operator, 166–170, 172

BRST symmetry, 165–170, see also

action, symmetry of, fermionic

BRST-closed, 168

BRST-exact, 168

CPn,

see

Pn

and complex projective

space

CP1,

see

P1

and complex projective

line

C∞

manifold, see manifold,

C∞

Calabi-Yau manifold, 187

deﬁnition of, 174

example of, 175

Calabi-Yau threefold, 132, 173–177

deﬁnition of, 174

example of, 174

Gromov-Witten invariant of, 176

calculus of variations, 137

canonical bundle, 174, 184

category, 48

example of, 49, 50, 76

201

A-model, 163, 166, 176, 179, 180, 185

action, 169, 172

correlation function, 168–170, 189,

see also Gromov-Witten

invariant

fermionic symmetry of, see BRST

symmetry

observable, 169, 176

abelian group, 68

free, 70

homomorphism of, 69, 76

action, 136–137, 143, 146

bosonic string, see string theory,

bosonic, action

of A-model, see A-model, action

supersymmetric, 150, 151

symmetry of, 139, 141

continuous, 139

example of, 141

fermionic, 163

inﬁnitesimal, 140, 143

algebraic curve, 31

isomorphism of, 32

algebraic geometry, 9, 20

angular momentum, 141

antisymmetric product, 61, see also

wedge product

area form, 160, 171

arithmetic genus, 34

atlas, 50, 58, 60

B-model

correlation function, 177, 189

ball, 44, 45

Berezin integral, 149, 153, see also

fermionic integration

B´ ezout’s theorem, 16, 17, 19, 21, 22,

24, 41, 80–81, 193, 194, see also

enumerative geometry, in the

plane

big quantum cohomology, 191–196

product, 194

associativity of, 194–196

of

P1,

194–195

of

P2,

195–196

bosonic string action, see string

theory, bosonic, action

boundary, 54, 72

boundary operator, 71

branch point, 36, 38, 42

BRST cohomology, 166, 168

BRST operator, 166–170, 172

BRST symmetry, 165–170, see also

action, symmetry of, fermionic

BRST-closed, 168

BRST-exact, 168

CPn,

see

Pn

and complex projective

space

CP1,

see

P1

and complex projective

line

C∞

manifold, see manifold,

C∞

Calabi-Yau manifold, 187

deﬁnition of, 174

example of, 175

Calabi-Yau threefold, 132, 173–177

deﬁnition of, 174

example of, 174

Gromov-Witten invariant of, 176

calculus of variations, 137

canonical bundle, 174, 184

category, 48

example of, 49, 50, 76

201