220
Index
Gerstenhaber algebra, 41
Gerstenhaber bracket, 40
Graded dual, 92
Grading, 91
Graph, 117
H
Half-edges of a graph, 117
Hodge decomposition, 33
Homotopy involutive Lie bialgebra, 48
Homotopy Lie algebra , 37
I
Internal differential, 97, 176
Involutive Lie bialgebra, 209
J
Jacobi identity, 37
K
Koszul sign, 91
Koszul sign convention, 91
L
Labelled graph, 143
Labelling, 143
Leg of a graph, 117
Lie bialgebra, 209
Linearization of an operad, 105
Loop homotopy algebra, 8, 206
M
Markl-Voronov algebra, 213
Master equation, 41
Minimal area metric, 57
Minimal model, 47
Modular comodule, 171
Modular completion, 138
Modular cooperad, 171
Modular envelope, 138
Modular module, 133
Modular operad, 134, 145
Module over an operad, 159
Moduli space, 38
Montreal monoidal structure, 149
Morphism of graphs, 119
Morphisms of cyclic operads, 98
Morphisms of IBL ∞ -algebras, 212
O
Odd cyclic operad, 156
Odd modular operad, 148
On-shell condition, 13
Open-closed homotopy algebra, 8
Operad algebra, 131, 142, 154
Operadic genus, 133
Operadic ideal, 124
Operator product expansion, 30
Operator-state correspondence, 56
Opposite monoidal structure, 150
Order k derivation, 207
P
Physical state, 13, 31, 56
Physical subspace, 31
Planar graph, 127
Propagator, 32
Q
Quantum-closed operad, 138
Quantum L ∞ -algebra, 8
Quantum-mechanical states, 12
Quasi-isomorphism, 19
R
Renormalisable theory, 38
S
S-channel, 59
Schiffer variation, 43
Semi-relative cohomology, 31
Shuffle, 40
Siegel gauge, 31
Stable curve, 137
Stable cyclic operad, 104
Stable modular operad, 136
Stable non-Σ cyclic operad, 126
Step of a modular operad, 134
String tension, 27
Strongly homotopy Lie algebra, 47, 206
Suboperad, 124
Suspension, 93
Symmetric group, 91
Symmetrization, 127
Symplectic transformation, 15
Index
Gerstenhaber algebra, 41
Gerstenhaber bracket, 40
Graded dual, 92
Grading, 91
Graph, 117
H
Half-edges of a graph, 117
Hodge decomposition, 33
Homotopy involutive Lie bialgebra, 48
Homotopy Lie algebra , 37
I
Internal differential, 97, 176
Involutive Lie bialgebra, 209
J
Jacobi identity, 37
K
Koszul sign, 91
Koszul sign convention, 91
L
Labelled graph, 143
Labelling, 143
Leg of a graph, 117
Lie bialgebra, 209
Linearization of an operad, 105
Loop homotopy algebra, 8, 206
M
Markl-Voronov algebra, 213
Master equation, 41
Minimal area metric, 57
Minimal model, 47
Modular comodule, 171
Modular completion, 138
Modular cooperad, 171
Modular envelope, 138
Modular module, 133
Modular operad, 134, 145
Module over an operad, 159
Moduli space, 38
Montreal monoidal structure, 149
Morphism of graphs, 119
Morphisms of cyclic operads, 98
Morphisms of IBL ∞ -algebras, 212
O
Odd cyclic operad, 156
Odd modular operad, 148
On-shell condition, 13
Open-closed homotopy algebra, 8
Operad algebra, 131, 142, 154
Operadic genus, 133
Operadic ideal, 124
Operator product expansion, 30
Operator-state correspondence, 56
Opposite monoidal structure, 150
Order k derivation, 207
P
Physical state, 13, 31, 56
Physical subspace, 31
Planar graph, 127
Propagator, 32
Q
Quantum-closed operad, 138
Quantum L ∞ -algebra, 8
Quantum-mechanical states, 12
Quasi-isomorphism, 19
R
Renormalisable theory, 38
S
S-channel, 59
Schiffer variation, 43
Semi-relative cohomology, 31
Shuffle, 40
Siegel gauge, 31
Stable curve, 137
Stable cyclic operad, 104
Stable modular operad, 136
Stable non-Σ cyclic operad, 126
Step of a modular operad, 134
String tension, 27
Strongly homotopy Lie algebra, 47, 206
Suboperad, 124
Suspension, 93
Symmetric group, 91
Symmetrization, 127
Symplectic transformation, 15