Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2).
John Henry SchwarzRelated topics
case compact dim example found general group map number question rule scalar space subgroup symmetry theory thus type global maximal fields space-time supergravityRelated quotes
I think of my pictures as dramas; the shapes in the pictures are the performers. They have been created from the need for a group of actors who are able to move dramatically without embarrassment and execute gestures without shame. Neither the action nor the actors can be anticipated, or described in advance. They begin a an unknown adventure in an unknown space... Ideas and plans that existed in the mind at the start were simply the doorway through which one left the world in which they occur. The great cubist pictures thus transcend and belie the implications of the cubist program.
Mark Rothko
Among the many senses that modern painters have lost, we must number the sense of architecture. The edifice accompanying the human figure, whether alone or in a group, whether in a scene from life or in an historical drama, was a great concern of the ancients. They applied themselves to it with loving and severe spirit, studying and perfecting the laws of perspective. A landscape enclosed in the arch of a portico or in the square or rectangle of a window acquires a greater metaphysical value, because it is solidified and isolated from the surrounding space. Architecture completes nature.
Giorgio de Chirico
Now, in the unhindered and unobstructed dharma-opening of the dharma-realm there is no dharma, and yet no non-dharma; no opening, and yet no non-opening. Thus it is neither large nor small, neither in a hurry nor taking its time; neither moving nor still, neither one nor many. Since it its not large, it can become an atom, leaving nothing behind. Since it is not small, it can contain all of space with room left over. Unhurried, it can include all the kalpas in the three time periods; not taking its time, it can enter fully into an instant.
Wonhyo
The first question that offers itself is, whether the general form and aspect of the government be strictly republican. It is evident that no other form would be reconcilable with the genius of the people of America; with the fundamental principles of the Revolution; or with that honorable determination which animates every votary of freedom, to rest all our political experiments on the capacity of mankind for self-government. If the plan of the convention, therefore, be found to depart from the republican character, its advocates must abandon it as no longer defensible.
James Madison
We can regard the vector ci as representing certain physical, social, and psychological attributes of player i himself in that it summarizes some crucial parameters of player i's own payoff function Ui as well as the main parameters of his beliefs about his social and physical environment... the rules of the game as such allow any given player i to belong to any one of a number of possible types, corresponding to the alternative values of his attribute vector c i could take... Each player is assumed to know his own actual type but to be in general ignorant about the other players' actual types.
John Harsanyi
