What Is String Theory?

String theory is a theoretical framework in physics that proposes that the fundamental constituents of nature are not zero-dimensional point particles but one-dimensional extended objects called strings. Different vibrational modes of a string correspond to different particles: a string vibrating in one configuration appears as an electron, while the same string vibrating in a different mode appears as a photon or a graviton. This substitution resolves a deep problem in twentieth-century physics: the mathematical incompatibility between quantum mechanics, which governs the behavior of matter at subatomic scales, and general relativity, which describes gravity and the geometry of spacetime. String theory incorporates gravity naturally as a quantum mechanical theory because the graviton, the carrier of the gravitational force, emerges as one of the string's vibrational modes.

The theoretical development of string theory began in the late 1960s as an attempt to model the strong nuclear force. After quantum chromodynamics (QCD) displaced it from that role in the 1970s, string theory was reformulated as a candidate for a unified description of all four fundamental forces. The NASA Imagine the Universe overview of superstrings describes how a 1996 calculation by Strominger and Vafa used string theory to reproduce the Bekenstein-Hawking entropy formula for black holes, providing the first concrete quantitative prediction from the framework.

Fundamental Strings and Vibrational Modes

A string in string theory has a characteristic length scale, the string length, which is thought to be on the order of the Planck length, roughly 10 to the negative 35 meters, far below the resolution of any existing or foreseeable particle accelerator. Open strings have two free endpoints; closed strings form loops with no endpoints. The tension of the string, an intrinsic parameter of the theory, determines the mass spectrum of the particles corresponding to different vibrational modes. At low energies, the excited modes are extremely massive and unobservable, so only the lowest-energy vibrational states, which correspond to known particles, are relevant to observable physics. Supersymmetry, a symmetry relating bosons and fermions, is required for the mathematical consistency of the most developed string theories; the resulting frameworks are called superstring theories.

Extra Dimensions and Compactification

Consistent superstring theories require ten spacetime dimensions: one time dimension and nine spatial dimensions. Since ordinary experience perceives only three spatial dimensions, the six additional spatial dimensions must be compactified, curled up at a scale too small to detect with current instruments. The geometry of the compactified dimensions determines which particles and forces appear in the four-dimensional effective theory. A vast number of possible compactification geometries, each yielding a different low-energy physics, constitute what is called the string theory landscape. Selecting which compactification corresponds to the actual universe is an open problem; it is related to the vacuum selection problem and remains one of the central challenges in the field. The Cambridge University lecture notes on string theory by David Tong provide a rigorous graduate-level treatment of the bosonic string, superstring theories, and the role of extra dimensions in the mathematical structure of the framework.

String Theory and Quantum Gravity

The most significant achievement of string theory is its provision of a consistent quantum theory of gravity. In conventional quantum field theory, attempts to quantize general relativity produce infinities that cannot be renormalized; string theory avoids these divergences because the spatial extent of strings smooths out the ultra-short-distance singularities that cause the infinities. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, proposed by Juan Maldacena in 1997, established a precise mathematical equivalence between a string theory in a particular curved spacetime and a quantum field theory on the boundary of that space. This correspondence has found applications in condensed matter physics and nuclear physics well beyond its original motivation. A discussion of string theory's status and open questions is available at Penn Today's overview.

Applications

String theory has theoretical and applied connections across a range of physics research areas, including:

• Black hole thermodynamics and the statistical origin of black hole entropy
• Quantum chromodynamics at strong coupling via AdS/CFT duality
• Condensed matter physics models of strongly correlated electron systems
• Cosmological models of the early universe and inflation
• Mathematical physics, including advances in algebraic geometry and topology arising from string compactification studies