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Movements, leaders, victories and the continuing fight for equality.
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Movements, leaders, victories and the continuing fight for equality.
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In August 1908, a white mob attacked Springfield, Illinois’s Black community, destroying homes and businesses and lynching two Black men. National outrage over the violence helped spur the movement that created the NAACP the following year.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
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| Fundamental objects |
| Perturbative theory |
| Non-perturbative results |
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In physics, matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U(N) for a large value of N. This matrix string theory was first proposed by Luboš Motl in 1997[1] and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde.[2] Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya.[3]
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In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have N = 2 {\displaystyle {\mathcal {N}}=2} extended supersymmetry which is maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection. They were first discovered by Michael Green and John Henry Schwarz in 1982, with the terminology of type I and type II coined to classify the three string theories known at the time.
In supersymmetry, type IIB supergravity is the unique supergravity in ten dimensions with two supercharges of the same chirality. It was first constructed in 1983 by John Schwarz and independently by Paul Howe and Peter West at the level of its equations of motion. While it does not admit a fully covariant action due to the presence of a self-dual field, it can be described by an action if the self-duality condition is imposed by hand on the resulting equations of motion. The other types of supergravity in ten dimensions are type IIA supergravity, which has two supercharges of opposing chirality, and type I supergravity, which has a single supercharge. The theory plays an important role in modern physics since it is the low-energy limit of type IIB string theory.
In physics, matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U(N) for a large value of N. This matrix string theory was first proposed by Luboš Motl in 1997 and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde. Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya.
In theoretical physics orientifold is a generalization of the notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element(s) of the orbifold group includes the reversal of the orientation of the string. Orientifolding therefore produces unoriented strings—strings that carry no "arrow" and whose two opposite orientations are equivalent. Type I string theory is the simplest example of such a theory and can be obtained by orientifolding type IIB string theory. In mathematical terms, given a smooth manifold M {\displaystyle {\mathcal {M}}} , two discrete, freely acting, groups G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} and the worldsheet parity operator Ω p {\displaystyle \Omega _{p}} (such that Ω p : σ → 2 π − σ {\displaystyle \Omega _{p}:\sigma \to 2\pi -\sigma } ) an orientifold is expressed as the quotient space M / ( G 1 ∪ Ω G 2 ) {\displaystyle {\mathcal {M}}/(G_{1}\cup \Omega G_{2})} . If G 2 {\displaystyle G_{2}} is empty, then the quotient space is an orbifold. If G 2 {\displaystyle G_{2}} is not empty, then it is an orientifold.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Joe Louis.