In general, is Libertarian ideology for or against the idea of the antitrust law?
Libertarianism is in concept against anti-trust law; for 2 reasons:
Using the power of the state to compel private entity to alter non-criminal behavior is against Non-Aggression Principle.
Please note that this specifically applies to "you can't merge" / "you can't be larger than X" antitrust laws.
Libertarians can still support anti-trust laws that amount to prohibition of monopolistic behavior which violates NAP (e.g. if a monopoly sends goons to dissuade customers from using competitor's products, that's within libertarian-supported concept of things there should be laws against - but it's not about the monopoly part but about goon part).
More interestingly, most libertarians posit that, under proper free market, monopolies wouldn't even exist for most part.
Basically, nearly 100% of examples of existing monopolies are NOT a monopoly that would occur under free market and libertarian government; and instead are a result of a company using rent-seeking or other market-distorting government behavior to obtain and more importantly keep the monopolistic position. "The Myth of Natural Monopoly" by Thomas J. DiLorenzo covers the topic pretty well; analyzing many common examples of monopolies in this light.
At birds-eye view, this stems not so much from libertarian philosophy itself; and more from free-market economics approach inherent in it. Basically, a monopoly can only arise when a competitor cannot provide a specific good or service at better price/value point than the monopolist. But that's nearly impossible to achieve at large scale absent government distortions (you can have local monopoly by owning a majority of scarce resource whose alternatives are all more expensive; for example by owning the only suitable land for a good port in a city. But that won't stop competition from arising from railways, airships, etc... - meaning, you as a port monopoly can't raise your prices indefinitely which is the reason monopoly is a thing).
Some libertarians see anti-trust in a very different light than most people.They see anti-trust legislation not as protecting consumers, but as cronyist regulation protecting competitors from honest competition by large efficient, low price firms. It's not that they don't see the purpose of anti-trust in theory, it's that they see government as far too inefficient and corrupt to use the power of anti-trust for the good of consumers. For example, in the econ talk podcast Don Boudreaux argues:
History of anti-trust laws: ... Common view is that you had the robber barons, and they had monopolies, they were exploiting the consumer so the government had to step in to help the consumer. The railroad, the telegraph, personalities, the Carnegies, the Rockefellers; government just couldn't let it go on, so we'll pass the Sherman Act because we care about consumers ...Tom DiLorenzo, 1985 article in International Review of Law and Economics [found] No evidence of monopoly [in] Standard Oil, American Tobacco, Carnegie Steel. They were growing and had big market shares but in fact they didn't have monopolies and they were benefiting consumers, as evidenced by their price declines. Gary Libecap, economic historian, at Arizona, came to same conclusion. The [anti-trust] legislation got sparked by the meat packing industries. Gustafus Swift had [a] brainstorm that by centralizing the slaughter of beef, chicken, and pork he could make a lot of money. Very quickly [he] was shipping beef, refrigerated railroad cars helped [bring down the] prices of beef[.] from 1879 to 1886 price had fallen by 30% in real terms for consumer[s]. Local butchers were undercut; and other meat-packing competitors sprang up. Explosive industry. Reaction to that industry sparked anti-trust. [The] Economy was becoming so much more competitive that the old-line producers complained and got the ear of legislators, giving rise to antitrust. Antitrust was an attempt to halt that competition.
Here's another example from the very libertarian Library of Economics and Liberty arguing that anti-trust legislation benefits competitors of efficient firms.
One of the most worrisome statistics in antitrust is that for every case brought by government, private plaintiffs bring ten. The majority of cases are filed to hinder, not help, competition. According to Steven Salop, formerly an antitrust official in the Carter administration, and Lawrence J. White, an economist at New York University, most private antitrust actions are filed by members of one of two groups. The most numerous private actions are brought by parties who are in a vertical arrangement with the defendant (e.g., dealers or franchisees) and who therefore are unlikely to have suffered from any truly anticompetitive offense. Usually, such cases are attempts to convert simple contract disputes (compensable by ordinary damages) into triple-damage payoffs under the Clayton Act.
The second most frequent private case is that brought by competitors. Because competitors are hurt only when a rival is acting procompetitively by increasing its sales and decreasing its price, the desire to hobble the defendant’s efficient practices must motivate at least some antitrust suits by competitors. Thus, case statistics suggest that the anticompetitive costs from “abuse of antitrust,” as New York University economists William Baumol and Janusz Ordover (1985) referred to it, may actually exceed any procompetitive benefits of antitrust laws.
They also argue that anti-trust cases are used by politicians to keep factories and headquarters alive in their local areas at the expense of nationwide consumers.
If public-interest rationales do not explain antitrust, what does? A final set of studies has shown empirically that patterns of antitrust enforcement are motivated at least in part by political pressures unrelated to aggregate economic welfare. For example, antitrust is useful to politicians in stopping mergers that would result in plant closings or job transfers in their home districts.
"Generally", libertarianism supports free markets. In a free market, there is no need for anti-trust laws. For example, anti-trust law (in the US) says no monopolies. If a monopoly exists in an actual free market it is because other companies cannot compete on price or service. That's a good monopoly.
There are two ways to attain an exclusive position in the market, that is to say, there are two ways to achieve monopoly. One way is not only harmless—indeed, it is beneficial; the other is bad. The beneficial way is to become superior to everyone else in providing some good or service.
Antitrust laws also attempt to prevent collusion and mergers that would reduce competition. In this sense it is the same as a monopoly and the answer is as above. If there is no barrier to entry the market regulates itself.