Introduction to Superstring Theory

Exact black five-branes in critical superstring theory

Physical Review Letters ◽

10.1103/physrevlett.67.2930 ◽

1991 ◽

Vol 67 (21) ◽

pp. 2930-2932 ◽

Cited By ~ 36

Author(s):

Steven B. Giddings ◽

Andrew Strominger

Keyword(s):

Superstring Theory

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New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)212 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Shai M. Chester ◽

Michael B. Green ◽

Silviu S. Pufu ◽

Yifan Wang ◽

Congkao Wen

Keyword(s):

Eisenstein Series ◽

Mass Parameter ◽

Flat Space ◽

Superstring Theory ◽

Modular Invariant ◽

Yang Mills ◽

Laplace Eigenvalue ◽

Modular Invariants ◽

Tensor Multiplet ◽

Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

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ANOMALOUS U(1)A AND ELECTROWEAK SYMMETRY BREAKING

Modern Physics Letters A ◽

10.1142/s0217732301004005 ◽

2001 ◽

Vol 16 (13) ◽

pp. 835-844

Author(s):

ILIA GOGOLADZE ◽

MIRIAN TSULAIA

Keyword(s):

Gauge Symmetry ◽

Standard Model ◽

Symmetry Breaking ◽

Supersymmetric Standard Model ◽

Electroweak Symmetry Breaking ◽

Electroweak Symmetry ◽

Superstring Theory

We suggest a new mechanism for electroweak symmetry breaking in the supersymmetric Standard Model. Our suggestion is based on the presence of an anomalous U (1)A gauge symmetry, which naturally arises in the four-dimensional superstring theory, and heavily relies on the value of the corresponding Fayet–Illiopoulos ξ-term.

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Ricci-flat compactifications in superstring theory and coxeter automorphisms. II

Theoretical and Mathematical Physics ◽

10.1007/bf01016979 ◽

1988 ◽

Vol 77 (3) ◽

pp. 1247-1259

Author(s):

D. G. Markushevich ◽

M. A. Ol'shanetskii ◽

A. M. Perelomov

Keyword(s):

Superstring Theory ◽

Ricci Flat

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Dimensional reductions of superstring theory

Nuclear Physics B ◽

10.1016/0550-3213(86)90375-5 ◽

1986 ◽

Vol 273 (3-4) ◽

pp. 537-551 ◽

Cited By ~ 5

Author(s):

David Bailin ◽

Alex Love ◽

Steven Thomas

Keyword(s):

Superstring Theory

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The effective action for the 4-point functions in abelian open superstring theory

Journal of High Energy Physics ◽

10.1088/1126-6708/2003/08/036 ◽

2003 ◽

Vol 2003 (08) ◽

pp. 036-036 ◽

Cited By ~ 4

Author(s):

Mees de Roo ◽

Martijn G.C Eenink

Keyword(s):

Effective Action ◽

Superstring Theory

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In quest of higher dimensions – Superstring Theory and the Calabi – Yau manifolds

10.31219/osf.io/tcb3y ◽

2021 ◽

Author(s):

Deep Bhattacharjee ◽

Sanjeevan Singha Roy

Keyword(s):

String Theory ◽

Higher Dimensions ◽

Physical Reality ◽

Space Time ◽

Superstring Theory ◽

Real Nature ◽

Time Space ◽

Klein Theory ◽

Relative Notion ◽

Definition Of

Higher dimensions are impossible to visualize as the size of dimension varies inversely proportional to its level. The more the dimension ranges, the least its size. We are a set of points living in a particular point of space and a particular frame of time. i.e, we live in space-time. The space has more dimensions that meets the human eye. We are living in a world of hyper-space. Our world being a smaller dimension is floating in higher dimensions. The quest for the visually of higher dimensions has been a fantasy to mankind but this aspect of nature is completely locked. We can transform dimensions i.e., from higher to lower dimensions, or from lower to higher dimensions, but only through mathematics. The relative notion of mathematics helps us to do the thing, which is perhaps impossible in the experimental part of physical reality. Humans being an element of 3 Dimensions – length, breath, height can only perceive one higher dimensions, that is space-time. but beyond that the notion of dimension itself changes. The dimensions got curled up in every intersection of the coordinates of space in such a way that the higher dimensions remain stable to us. But in reality it is highly unstable. In the higher dimensions, above 4, the space is tearing apart and joining again spontaneously, but the tearing portion itself covered by 2 dimensional Branes which acts as a stabilizer for the unstable dimensions. Dimensions will get smaller and smaller with the space-time interwoven in it. But at Planks length that is 10^-33 meter, the notion of space-time itself breaks down thereby making impossible for the higher dimensions to coexist along with space. Without space, there will be no identity of any dimension. The space itself is the fabric for the milestone of residing higher dimensions. Imagine our room, which is 3 dimensional. But what is there inside the room. The space and of course the time. Space-time being a totally separate entity is not quite separate when compared with other dimensions because it makes the residing place for the higher dimensions or the hyperspace itself. We all are confined within a lower dimensional world within a randomness of higher dimensions. Time being alike like space is an arrow which has the capability of slicing space into different forms. Thereby taking a snapshot of our every nano-second we vibrate within space-time. As each slice of time represents each slice of space, similarly each slice of space represents each slice of time. The nature of space-time is beyond human consciousness. It is the identity by which we breathe, we play, we survive. It is the whole localization of species that encompasses itself with space thereby making space-time a relative quantity depending upon the reference frame. The only thing that can encompass space-time or even change the relative definition of space-time is the speed, the speed far beyond the speed of light. The more the speed, the less the array of time flows. Space-time being an invisible entity makes the other dimensions visible residing in it only into the level of 3, that is l, b, h. After that there is a infamous structure formed by the curling of higher dimensions called CALABI-YAU manifold. This manifold depicts the usual nature of the dimensional quadrants of the higher order by containing a number of small spherical spheres inside it. The mathematics of string theory is still unable to solve the genus and the containing spheres of the manifold which can be the ultimate quest for the hidden dimensions. Hidden, as, the higher dimensions are hidden from human perspective of macro level but if we probe deeper into the fabric of the space-time of General Relativity then we will find the 5th dimension according to the Kaluza-Klein theory. And if we probe even deeper into it at the perspective of string theory we will be amazed to see the real nature of quantum world. They are so marvelously beautiful, they contain so many forms of higher dimensions ranging from 6 to 10. And even many more of that, but we are still not sure about it where they may exist in a ghost state. After all, the quantum nature is far more beautiful that one can even imagine with a full faze of weirdness.

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